Robert A. Van Gorder

Generating author description...

All published works

Action	Title	Year	Authors
+	Macroscopic description of a heavy particle immersed within a flow of light particles	2023	Radek Erban Robert A. Van Gorder
+ PDF Chat	Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation	2022	Joshua Ritchie Andrew L. Krause Robert A. Van Gorder
+ PDF Chat	Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged	2022	Robert A. Van Gorder
+	Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	2022	Robert A. Van Gorder
+ PDF Chat	Homogenised model for the electrical current distribution within a submerged arc furnace for silicon production	2021	Ellen K. Luckins James M. Oliver Colin P. Please Benjamin M. Sloman Robert A. Van Gorder
+	Controlling the motion of a travelling wave.	2021	Robert A. Van Gorder
+ PDF Chat	On the sum of positive divisors functions	2021	Radek Erban Robert A. Van Gorder
+ PDF Chat	Turing conditions for pattern forming systems on evolving manifolds	2021	Robert A. Van Gorder Václav Klika Andrew L. Krause
+ PDF Chat	A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns	2020	Nick P. Taylor Hyunyeon Kim Andrew L. Krause Robert A. Van Gorder
+ PDF Chat	A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations	2020	Andrew L. Krause Robert A. Van Gorder
+ PDF Chat	Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices	2020	Robert A. Van Gorder Andrew L. Krause Boris A. Malomed D. J. Kaup
+	Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schr\"{o}dinger lattices	2020	Robert A. Van Gorder Andrew L. Krause Boris A. Malomed D. J. Kaup
+ PDF Chat	Generalist predator dynamics under kolmogorov versus non-Kolmogorov models	2019	Yifang Xu Andrew L. Krause Robert A. Van Gorder
+ PDF Chat	Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids	2019	Kristian Kiradjiev Svenn Anton Halvorsen Robert A. Van Gorder Sam Howison
+ PDF Chat	Amplitude death criteria for coupled complex Ginzburg–Landau systems	2019	Robert A. Van Gorder Andrew L. Krause James A. Kwiecinski
+	Non-autonomous Turing conditions for reaction-diffusion systems on evolving domains	2019	Robert A. Van Gorder Václav Klika Andrew L. Krause
+	Turing conditions for pattern forming systems on evolving manifolds	2019	Robert A. Van Gorder Václav Klika Andrew L. Krause
+	Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids.	2018	Kristian Kiradjiev Svenn Anton Halvorsen Robert A. Van Gorder Sam Howison
+ PDF Chat	Wave propagation and pattern formation in two-dimensional hexagonally-packed granular crystals under various configurations	2018	Tianshu Hua Robert A. Van Gorder
+ PDF Chat	Bifurcations and Dynamics Emergent From Lattice and Continuum Models of Bioactive Porous Media	2018	Andrew L. Krause Dmitry Beliaev Robert A. Van Gorder Sarah L. Waters
+ PDF Chat	Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series	2018	Matthew W. Perkins Robert A. Van Gorder
+ PDF Chat	Lattice and continuum modelling of a bioactive porous tissue scaffold	2018	Andrew L. Krause Dmitry Beliaev Robert A. Van Gorder Sarah L. Waters
+ PDF Chat	Reproducing kernel method for the numerical solution of the 1D Swift–Hohenberg equation	2018	Parisa Bakhtiari S. Abbasbandy Robert A. Van Gorder
+ PDF Chat	Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains	2018	Armin Kekić Robert A. Van Gorder
+ PDF Chat	Coupled complex Ginzburg–Landau systems with saturable nonlinearity and asymmetric cross-phase modulation	2018	Robert A. Van Gorder Andrew L. Krause Ferran Brosa Planella Abigail M. Burton
+ PDF Chat	Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations	2018	Robert A. Van Gorder
+ PDF Chat	Chaos in a non-autonomous nonlinear system describing asymmetric water wheels	2018	Ashish Bhatt Robert A. Van Gorder
+ PDF Chat	Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations	2018	James A. Kwiecinski Attila Kovács Andrew L. Krause Ferran Brosa Planella Robert A. Van Gorder
+ PDF Chat	Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies	2018	Andrew L. Krause Lawrence Kurowski Kamran Yawar Robert A. Van Gorder
+	Generic amplitude death in coupled complex Ginzburg-Landau systems.	2018	Robert A. Van Gorder Andrew L. Krause James A. Kwiecinski
+	Amplitude death criteria for coupled complex Ginzburg-Landau systems	2018	Robert A. Van Gorder Andrew L. Krause James A. Kwiecinski
+ PDF Chat	Opinion formation and distribution in a bounded-confidence model on various networks	2018	Xiangyi Meng Robert A. Van Gorder Mason A. Porter
+	Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids	2018	Kristian Kiradjiev Svenn Anton Halvorsen Robert A. Van Gorder Sam Howison
+	Amplitude death criteria for coupled complex Ginzburg-Landau systems	2018	Robert A. Van Gorder Andrew L. Krause James A. Kwiecinski
+	Dynamics from a coupled complex Ginzburg-Landau system with saturable nonlinearity	2017	Robert A. Van Gorder Andrew L. Krause Ferran Brosa Planella Abigail M. Burton
+ PDF Chat	Solving the Dym initial value problem in reproducing kernel space	2017	Parisa Bakhtiari S. Abbasbandy Robert A. Van Gorder
+ PDF Chat	Solutions to Forced and Unforced Lin–Reissner–Tsien Equations for Transonic Gas Flows on Various Length Scales	2017	Kyle A. Theaker Robert A. Van Gorder
+	Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold	2017	Andrew L. Krause Dmitry Beliaev Robert A. Van Gorder Sarah L. Waters
+	Analysis of Lattice and Continuum Models of Bioactive Porous Media	2017	Andrew L. Krause Dmitry Beliaev Robert A. Van Gorder Sarah L. Waters
+	Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold	2017	Andrew L. Krause Dmitry Beliaev Robert A. Van Gorder Sarah L. Waters
+ PDF Chat	On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations	2016	Robert A. Van Gorder
+	Wave propagation across interfaces between two Hertz-like granular crystals with different interaction exponents	2016	Armin Kekić Robert A. Van Gorder
+ PDF Chat	Reduction of dimension for nonlinear dynamical systems	2016	Heather A. Harrington Robert A. Van Gorder
+ PDF Chat	Asymptotic solutions for a relativistic formulation of the generalized nonextensive Thomas–Fermi model	2016	Vanessa C. Lowry Robert A. Van Gorder
+	Reproducing kernel method for the numerical solution of the Brinkman–Forchheimer momentum equation	2016	S. Abbasbandy Robert A. Van Gorder Parisa Bakhtiari
+ PDF Chat	Fractional diffusion equation for an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-dimensional correlated Lévy walk	2016	Jake P. Taylor‐King Rainer Klages Sergei Fedotov Robert A. Van Gorder
+	The generalized Taylor series approach is not equivalent to the homotopy analysis method	2016	Robert A. Van Gorder
+	Jacobi–Gauss–Lobatto collocation method for solving nonlinear reaction–diffusion equations subject to Dirichlet boundary conditions	2015	A. H. Bhrawy E. H. Doha M. A. Abdelkawy Robert A. Van Gorder
+	Reduction of dimension for nonlinear dynamical systems	2015	Heather A. Harrington Robert A. Van Gorder
+ PDF Chat	Continuous periodic solution of a nonlinear pseudo-oscillator equation in which the restoring force is inversely proportional to the dependent variable	2015	Robert A. Van Gorder
+	Analytical construction of peaked solutions for the nonlinear evolution of an electromagnetic pulse propagating through a plasma	2015	Mathew Baxter Robert A. Van Gorder K. Vajravelu
+	Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system	2015	Mathew Baxter S. Roy Choudhury Robert A. Van Gorder
+ PDF Chat	Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation	2015	Robert A. Van Gorder
+	Self-similar solutions for the nonlinear dispersion of a chemical pollutant into a river flow	2015	Robert A. Van Gorder Kalie Makowski Kristina Mallory K. Vajravelu
+	A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation	2015	A. H. Bhrawy Mahmoud A. Zaky Robert A. Van Gorder
+	Efficient low-error analytical-numerical approximations for radial solutions of nonlinear Laplace equations	2015	John Haussermann Robert A. Van Gorder
+	The variational iteration method is a special case of the homotopy analysis method	2015	Robert A. Van Gorder
+	On existence and multiplicity of similarity solutions to a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow for decelerated flows	2015	R. Naseri Alaeddin Malek Robert A. Van Gorder
+ PDF Chat	Recent Advances in Solution Methods for Nonlinear Evolution Equations, Fluid Flow, and Heat and Mass Transfer	2015	S. S. Motsa Stanford Shateyi Robert A. Van Gorder Najib Laraqi B. Rush Kumar
+ PDF Chat	New Trends on Fractional and Functional Differential Equations	2015	Dumitru Băleanu Ali H Bhrawy Robert A. Van Gorder
+ PDF Chat	Recent Theory and Applications on Numerical Algorithms and Special Functions	2015	Ali H Bhrawy Robert A. Van Gorder Dumitru Băleanu Guo–Cheng Wu
+	Reduction of dimension for nonlinear dynamical systems	2015	Heather A. Harrington Robert A. Van Gorder
+	Relation between Lane–Emden solutions and radial solutions to the elliptic Heavenly equation on a disk	2014	Robert A. Van Gorder
+	Computing semi-commuting differential operators in one and multiple variables	2014	Robert A. Van Gorder
+	A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems	2014	A. H. Bhrawy E. H. Doha S. S. Ezz‐Eldien Robert A. Van Gorder
+	Does the Riemann zeta function satisfy a differential equation?	2014	Robert A. Van Gorder
+	Numerical Computation of Travelling Wave Solutions for the Nonlinear Ito System	2014	Ali H. Bhrawy Robert A. Van Gorder
+	Solution method for the transformed time-dependent Michaelis–Menten enzymatic reaction model	2014	Ronald Li Robert A. Van Gorder Kristina Mallory Kuppalappalle Vajravelu
+	The generalized lucky ticket problem, perfect matchings, and closure relations satisfied by the Chebyshev and $$q$$ q -Hermite polynomials	2014	Joseph P. Brennan Robert A. Van Gorder
+	Optimal analytic method for the nonlinear Hasegawa-Mima equation	2014	Mathew Baxter Robert A. Van Gorder K. Vajravelu
+	Small-Time Existence and Two Classes of Solutions for the $$n$$ n -Dimensional Coupled Yukawa Equations	2014	John Haussermann Robert A. Van Gorder
+	General exact solutions for linear and nonlinear waves in a Thirring model	2014	Robert A. Van Gorder
+	Bounds, monotonicity, uniqueness, and analytical calculation of a class of similarity solutions for the fluid flow over a nonlinearly stretching sheet	2014	Robert A. Van Gorder
+	Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation	2014	Robert A. Van Gorder
+	Jacobi–Gauss–Lobatto collocation method for the numerical solution of nonlinear Schrödinger equations	2014	E. H. Doha A. H. Bhrawy M. A. Abdelkawy Robert A. Van Gorder
+ PDF Chat	Exact and Approximate Solutions for Nonlinear PDEs	2014	Baojian Hong Dianchen Lu Chaudry Masood Khalique Alvaro H. Salas Robert A. Van Gorder
+ PDF Chat	An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry	2014	A. H. Bhrawy A. S. Alofi Robert A. Van Gorder
+	Editorial Exact and Approximate Solutions for Nonlinear PDEs	2014	Baojian Hong Dianchen Lu Chaudry Masood Khalique Alvaro H. Salas Robert A. Van Gorder
+	Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation	2014	Robert A. Van Gorder
+	Chapter 4: Stability of Auxiliary Linear Operator and Convergence-Control Parameter in the Homotopy Analysis Method	2013	Robert A. Van Gorder
+	Method for constructing analytical solutions to the Dym initial value problem	2013	Kristina Mallory Robert A. Van Gorder
+	Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere	2013	K. Reger Robert A. Van Gorder
+	The Cauchy problem for complex fuzzy differential equations	2013	Daria Karpenko Robert A. Van Gorder Abraham Kandel
+	A Jacobi rational pseudospectral method for Lane–Emden initial value problems arising in astrophysics on a semi-infinite interval	2013	E. H. Doha A. H. Bhrawy Ramy M. Hafez Robert A. Van Gorder
+	Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation	2013	Kristina Mallory Robert A. Van Gorder
+	Exact and analytical solutions for a nonlinear sigma model	2013	Mathew Baxter Robert A. Van Gorder
+	Competitive modes for the Baier–Sahle hyperchaotic flow in arbitrary dimensions	2013	Hassan Saberi Nik Robert A. Van Gorder
+	On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem	2013	Mathew Baxter Robert A. Van Gorder K. Vajravelu
+	Orbital Stability for Stationary Solutions of the Wadati–Konno–Ichikawa–Shimizu Equation	2013	Robert A. Van Gorder
+	Hyper-Riccati equations and integrable reductions permitting stationary solutions for complex hyperbolic field equations	2013	Kyle A. Theaker Robert A. Van Gorder
+	Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields	2013	Mathew Baxter Robert A. Van Gorder
+	Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems	2013	Matthew Russo Robert A. Van Gorder
+	Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer	2013	K. Vajravelu Robert A. Van Gorder
+	Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation	2013	Kristina Mallory Robert A. Van Gorder
+ PDF Chat	Resonant solitons from the 3 × 3 operator	2012	D. J. Kaup Robert A. Van Gorder
+	Painlevé property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities	2012	Matthew Russo Robert A. Van Gorder S. Roy Choudhury
+	Chemically reactive solute transfer in a moving fluid over a moving surface	2012	Swati Mukhopadhyay K. Vajravelu Robert A. Van Gorder
+	Painlevé test, integrability, and exact solutions for density-dependent reaction–diffusion equations with polynomial reaction functions	2012	Jessica Hearns Robert A. Van Gorder S. Roy Choudhury
+	A Multicomplex Riemann Zeta Function	2012	Lyall Reid Robert A. Van Gorder
+	Classical implicit travelling wave solutions for a quasilinear convection–diffusion equation	2012	Jessica Hearns Robert A. Van Gorder
+	Existence results for coupled nonlinear systems approximating the rotating MHD flow over a rotating sphere near the equator	2012	Hamid Bellout K. Vajravelu Robert A. Van Gorder
+	Asymptotic solutions for singularly perturbed Boussinesq equations	2012	John Haussermann Robert A. Van Gorder
+ PDF Chat	Erratum to: Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium	2012	Robert A. Van Gorder K. Vajravelu
+	Traveling wave solutions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" overflow="scroll"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mtext>,</mml:mtext><mml:mspace width="0.12em" /><mml:mi>v</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> to a generalized Drinfel’d–Sokolov system which satisfy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" overflow="scroll"><mml:mrow><mml:mi>u</mml:mi><mml:mo>=</…	2012	Erik Sweet Robert A. Van Gorder
+	Control of error in the homotopy analysis of semi-linear elliptic boundary value problems	2012	Robert A. Van Gorder
+	Stability analysis of the dual solutions for stagnation-point flow over a non-linearly stretching surface	2012	Tapas Ray Mahapatra Samir Kumar Nandy K. Vajravelu Robert A. Van Gorder
+ PDF Chat	Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices	2012	Boris A. Malomed D. J. Kaup Robert A. Van Gorder
+	Schrödinger equations on $${\mathbb{R}^3 \times \mathcal{M}}$$ with non-separable potential	2012	Robert A. Van Gorder
+	Unstaggered-staggered solitons in two-component discrete nonlinear Schr\	2012	Boris A. Malomed D. J. Kaup Robert A. Van Gorder
+	Principles of Homotopy Analysis	2012	K. Vajravelu Robert A. Van Gorder
+	Application of the Homotopy Analysis Method to Fluid Flow Problems	2012	K. Vajravelu Robert A. Van Gorder
+	Nonlinear Flow Phenomena and Homotopy Analysis	2012	K. Vajravelu Robert A. Van Gorder
+	Schrödinger equations on R 3 × M with non-separable potential	2012	Robert A. Van Gorder
+	Introduction	2012	K. Vajravelu Robert A. Van Gorder
+	Methods for the Control of Convergence in Obtained Solutions	2012	K. Vajravelu Robert A. Van Gorder
+	Steady revolving flow and heat transfer of a non-Newtonian Reiner–Rivlin fluid	2011	Bikash Sahoo Robert A. Van Gorder Helge I. Andersson
+	GLAISHER-TYPE PRODUCTS OVER THE PRIMES	2011	Robert A. Van Gorder
+	Self-similar solutions to Lin-Reissner-Tsien equation	2011	John Haussermann K. Vajravelu Robert A. Van Gorder
+	Computing the region of convergence for power series in many real variables: A ratio-like test	2011	Robert A. Van Gorder
+	Gaussian waves in the Fitzhugh–Nagumo equation demonstrate one role of the auxiliary function H(x,t) in the homotopy analysis method	2011	Robert A. Van Gorder
+	Exact first integrals for a Lane–Emden equation of the second kind modeling a thermal explosion in a rectangular slab	2011	Robert A. Van Gorder
+	Non-Darcian flow and heat transfer along a permeable vertical surface with nonlinear density temperature variation	2011	K. V. Prasad K. Vajravelu Robert A. Van Gorder
+	Resonant solitons from the $3\times 3$ operator	2011	D. J. Kaup Robert A. Van Gorder
+	Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet	2010	Robert A. Van Gorder K. Vajravelu Ioan Pop
+ PDF Chat	Wave functions and energy spectra for the hydrogenic atom in $\mathbb {R}^3 \times \mathcal {M}$ R3×M	2010	Robert A. Van Gorder
+	First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping	2010	Robert A. Van Gorder
+	Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System	2010	Robert A. Van Gorder S. Roy Choudhury
+	Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind	2010	Robert A. Van Gorder
+	Trigonometric and hyperbolic type solutions to a generalized Drinfel’d–Sokolov equation	2010	Erik Sweet Robert A. Van Gorder
+	Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet	2010	Robert A. Van Gorder K. Vajravelu F. Talay Akyıldız
+	Exponential-type solutions to a generalized Drinfel'd–Sokolov equation	2010	Erik Sweet Robert A. Van Gorder
+	Stability analysis of fluid flow over a nonlinearly stretching sheet	2010	Tapas Ray Mahapatra Samir Kumar Nandy K. Vajravelu Robert A. Van Gorder
+ PDF Chat	Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator	2010	Erik Sweet K. Vajravelu Robert A. Van Gorder
+	Analytical solutions to a generalized Drinfel’d–Sokolov equation related to DSSH and KdV6	2010	Erik Sweet Robert A. Van Gorder
+	Analytical solution for the unsteady MHD flow of a viscous fluid between moving parallel plates	2010	Erik Sweet K. Vajravelu Robert A. Van Gorder Ioan Pop
+	Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks	2010	Robert A. Van Gorder Erik Sweet K. Vajravelu
+	Analytical and numerical solutions of the density dependent Nagumo telegraph equation	2010	Robert A. Van Gorder K. Vajravelu
+	Analytical and numerical results for the Swift–Hohenberg equation	2010	F. Talay Akyıldız Dennis A. Siginer K. Vajravelu Robert A. Van Gorder
+	Recursive Relations for Bell Polynomials of Arbitrary Positive Non-Integer Order	2010	Robert A. Van Gorder
+	1 and Generalizations	2010	Robert A. Van Gorder
+	Integration Identities for Some Iterated Exponentials of Order Three	2010	Robert A. Van Gorder
+	A variational formulation of the Nagumo reaction–diffusion equation and the Nagumo telegraph equation	2009	Robert A. Van Gorder K. Vajravelu
+	A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet	2009	Robert A. Van Gorder K. Vajravelu
+	Existence and uniqueness results for a nonlinear differential equation arising in MHD Falkner–Skan flow	2009	Robert A. Van Gorder K. Vajravelu
+	Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium	2009	Robert A. Van Gorder K. Vajravelu
+	Computation of certain infinite series of the form for arbitrary real-valued k	2009	Robert A. Van Gorder
+	Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet	2009	F. Talay Akyıldız Dennis A. Siginer K. Vajravelu John R. Cannon Robert A. Van Gorder
+	On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach	2009	Robert A. Van Gorder K. Vajravelu
+	Implicit differential equation arising in the steady flow of a Sisko fluid	2009	F. Talay Akyıldız K. Vajravelu R. N. Mohapatra Erik Sweet Robert A. Van Gorder
+	Third-order partial differential equations arising in the impulsive motion of a flat plate	2008	Robert A. Van Gorder K. Vajravelu
+	Analytic and numerical solutions to the Lane–Emden equation	2008	Robert A. Van Gorder K. Vajravelu
+	Analytical and numerical solutions of the density dependent diffusion Nagumo equation	2008	Robert A. Van Gorder K. Vajravelu

Common Coauthors

Coauthor	Papers Together
K. Vajravelu	31
Andrew L. Krause	22
Erik Sweet	8
A. H. Bhrawy	6
Mathew Baxter	6
D. J. Kaup	6
James A. Kwiecinski	5
Dmitry Beliaev	5
Kristina Mallory	5
Sarah L. Waters	5
John Haussermann	4
Boris A. Malomed	4
F. Talay Akyıldız	4
E. H. Doha	4
Ferran Brosa Planella	3
S. Abbasbandy	3
Kristian Kiradjiev	3
Heather A. Harrington	3
Svenn Anton Halvorsen	3
Parisa Bakhtiari	3
S. Roy Choudhury	3
Václav Klika	3
Ali H. Bhrawy	3
Sam Howison	3
Matthew Russo	2
Armin Kekić	2
Dumitru Băleanu	2
Abigail M. Burton	2
Dianchen Lu	2
Samir Kumar Nandy	2
Baojian Hong	2
Ioan Pop	2
Dennis A. Siginer	2
M. A. Abdelkawy	2
Tapas Ray Mahapatra	2
Chaudry Masood Khalique	2
K. Vajravelu	2
Alvaro H. Salas	2
Jessica Hearns	2
Kyle A. Theaker	2
Radek Erban	2
Ramy M. Hafez	1
S. Roy Choudhury	1
Kuppalappalle Vajravelu	1
James M. Oliver	1
Abraham Kandel	1
B. Rush Kumar	1
Matthew W. Perkins	1
K. Vajravelu	1
Xiangyi Meng	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Beyond Perturbation: Introduction to the Homotopy Analysis Method	2004	Shijun Liao S. A. Sherif	28
+	On the homotopy analysis method for nonlinear problems	2003	Shijun Liao	27
+	An explicit, totally analytic approximate solution for Blasius’ viscous flow problems	1999	Shijun Liao	26
+	On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach	2009	Robert A. Van Gorder K. Vajravelu	26
+ PDF Chat	A General Approach to Obtain Series Solutions of Nonlinear Differential Equations	2007	Shijun Liao Yue Gang Tan	24
+	Notes on the homotopy analysis method: Some definitions and theorems	2008	Shijun Liao	24
+	Analytic and numerical solutions to the Lane–Emden equation	2008	Robert A. Van Gorder K. Vajravelu	22
+	AN EXPLICIT TOTALLY ANALYTIC APPROXIMATION OF BLASIUS VISCOUS FLOW PROBLEMS	1999	Shijun Liao	17
+	An optimal homotopy-analysis approach for strongly nonlinear differential equations	2009	Shijun Liao	17
+	A new analytic algorithm of Lane–Emden type equations	2003	Shijun Liao	16
+	A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate	1999	Shijun Liao	16
+	The application of homotopy analysis method to nonlinear equations arising in heat transfer	2006	S. Abbasbandy	16
+	Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt	2006	Muhammad Sajid Tasawar Hayat S. Asghar	16
+	Analytical solutions to a generalized Drinfel’d–Sokolov equation related to DSSH and KdV6	2010	Erik Sweet Robert A. Van Gorder	15
+	Implicit differential equation arising in the steady flow of a Sisko fluid	2009	F. Talay Akyıldız K. Vajravelu R. N. Mohapatra Erik Sweet Robert A. Van Gorder	15
+	Homotopy analysis method for heat radiation equations	2007	S. Abbasbandy	15
+	Homotopy Analysis Method in Nonlinear Differential Equations	2012	Shijun Liao	15
+	Gaussian waves in the Fitzhugh–Nagumo equation demonstrate one role of the auxiliary function H(x,t) in the homotopy analysis method	2011	Robert A. Van Gorder	14
+	Soliton solutions for the fifth-order KdV equation with the homotopy analysis method	2007	S. Abbasbandy F. Samadian Zakaria	14
+	Solving solitary waves with discontinuity by means of the homotopy analysis method	2005	Wan Wu Shijun Liao	14
+	Control of error in the homotopy analysis of semi-linear elliptic boundary value problems	2012	Robert A. Van Gorder	14
+	Homotopy analysis method for singular IVPs of Emden–Fowler type	2008	A. Sami Bataineh Mohd Salmi Md Noorani Ishak Hashim	13
+	Purely analytic solutions of the compressible boundary layer flow due to a porous rotating disk with heat transfer	2009	Mustafa Türkyılmazoğlu	13
+	Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method	2007	A. Sami Bataineh Mohd Salmi Md Noorani Ishak Hashim	13
+	Analytic solutions of the temperature distribution in Blasius viscous flow problems	2002	Shijun Liao Antonio Campo	13
+	Series solutions of nano boundary layer flows by means of the homotopy analysis method	2008	Jun Cheng Shijun Liao R. N. Mohapatra K. Vajravelu	13
+	On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder	2006	Tasawar Hayat M. Sajid	13
+	Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method	2004	Yongyan Wu Chun Wang Shijun Liao	12
+	The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear age-structured population models	2011	Mohammad Ghoreishi A. I. B. MD. Ismail A‎. ‎K‎. Alomari A. Sami Bataineh	11
+	Mathematical properties of -curve in the frame work of the homotopy analysis method	2011	S. Abbasbandy Elyas Shivanian K. Vajravelu	10
+	Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer	2013	K. Vajravelu Robert A. Van Gorder	8
+	Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation	2013	Kristina Mallory Robert A. Van Gorder	7
+	Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow	1961	Byron C. Sakiadis	7
+	Exponential-type solutions to a generalized Drinfel'd–Sokolov equation	2010	Erik Sweet Robert A. Van Gorder	7
+	An effective approach for approximate analytical solutions of the damped Duffing equation	2012	Mustafa Türkyılmazoğlu	7
+	Fluid flow over a nonlinearly stretching sheet	2006	K. Vajravelu John R. Cannon	7
+	Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation	2013	Kristina Mallory Robert A. Van Gorder	7
+	Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations	2007	M. Sajid Tasawar Hayat	7
+	The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation	2006	S. Abbasbandy	6
+	Approximate implicit solution of a Lane-Emden equation	2006	E. Momoniat C. Harley	6
+	Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind	2010	Robert A. Van Gorder	6
+	Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables	1965	D. B. Owen Milton Abramowitz Irene A. Stegun	6
+	The Painlevé property for partial differential equations	1983	John Weiss M. Tabor G. F. Carnevale	5
+	Analytical and numerical solutions of the density dependent diffusion Nagumo equation	2008	Robert A. Van Gorder K. Vajravelu	5
+	The Painlevé property and singularity analysis of integrable and non-integrable systems	1989	A. Ramani B. Grammaticos Tassos Bountis	5
+	A new algorithm for solving differential equations of Lane–Emden type	2001	Abdul‐Majid Wazwaz	5
+	Accurate computation of traveling wave solutions of some nonlinear diffusion equations	2006	M.B.A. Mansour	5
+	Soliton solutions for the Fitzhugh–Nagumo equation with the homotopy analysis method	2007	S. Abbasbandy	5
+	Homotopy analysis method for fractional IVPs	2007	Ishak Hashim O. Abdulaziz Shaher Momani	5
+	Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet	2009	F. Talay Akyıldız Dennis A. Siginer K. Vajravelu John R. Cannon Robert A. Van Gorder	5