Mathematics Numerical Analysis

Differential Equations and Numerical Methods

Description

This cluster of papers focuses on numerical methods and analysis for solving singularly perturbed problems, particularly in the context of convection-diffusion and reaction-diffusion equations. The research covers topics such as boundary layers, finite difference schemes, asymptotic analysis, parameter-robust methods, and adaptive meshes to accurately solve these challenging problems.

Keywords

Singular Perturbation; Numerical Methods; Convection-Diffusion Problems; Boundary Layers; Finite Difference Schemes; Asymptotic Analysis; Parameter-Robust Methods; Reaction-Diffusion Equations; Adaptive Meshes; Error Analysis

Most Cited Works

Action Title Date Authors
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Linear differential operators 1967-01-01 M. A. Naĭmark
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<i>Analysis of Numerical Methods</i> 1967-07-01 Eugene Isaacson Herbert B. Keller George H. Weiss
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Semigroups of Linear Operators and Applications to Partial Differential Equations 1983-01-01 A. Pazy
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Theory and applications of Hopf bifurcation 1981-01-01 Brian Hassard Nicholas D. Kazarinoff Yujie Wan
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Nonlinear Parabolic and Elliptic Equations 1993-01-01 C. V. Pao
Geometric Theory of Semilinear Parabolic Equations 1981-01-01 Daniel Henry
Perturbation Theory for Linear Operators 1995-01-01 Tosio Kato
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Perturbation Analysis of Optimization Problems 2000-01-01 J. Frédéric Bonnans Alexander Shapiro
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Methods of Bifurcation Theory 1982-01-01 Shui-Nee Chow Jack K. Hale
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Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems 2008-03-26 Hal L. Smith
Elliptic Partial Differential Equations of Second Order 2001-01-01 David Gilbarg Neil S. Trudinger
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Finite difference schemes and partial differential equations 1991-01-01 John C. Strikwerda
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SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS 2006-04-19 Ji‐Huan He
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Analysis of Fractional Differential Equations 2002-01-01 Kai Diethelm Neville J. Ford
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Linear and quasilinear elliptic equations 1968-01-01 O. A. Ladyzhenskai︠a︡ N. N. Uraltseva
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Variational iteration method – a kind of non-linear analytical technique: some examples 1999-07-01 Ji‐Huan He
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Geometric singular perturbation theory for ordinary differential equations 1979-01-01 Neil Fenichel
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Nonlinear Systems Analysis 1980-08-01 M. Vidyasagar C. Desoer
An integrable shallow water equation with peaked solitons 1993-09-13 Roberto Camassa Darryl D. Holm
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Weak solutions of nonlinear hyperbolic equations and their numerical computation 1954-02-01 Peter D. Lax
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Linear Partial Differential Operators 1963-01-01 Lars Hörmander
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On the Construction and Comparison of Difference Schemes 1968-09-01 Gilbert Strang
Existence of solitary waves in higher dimensions 1977-06-01 Walter A. Strauss
Perturbation Methods in Applied Mathematics 1973-11-01 Julian D. Cole Lawrence E. Levine
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Theory of Functional Differential Equations 1977-01-01 Jack K. Hale
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1983-01-01 John Guckenheimer Philip Holmes
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Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces 1976-10-01 Herbert Amann
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An iteration method for the solution of the eigenvalue problem of linear differential and integral operators 1950-10-01 Cornelius Lanczos
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Geometrical Methods in the Theory of Ordinary Differential Equations 1988-01-01 V. I. Arnold
Deterministic Nonperiodic Flow 1963-03-01 Edward N. Lorenz
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Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow 1961-03-01 Byron C. Sakiadis
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On the homotopy analysis method for nonlinear problems 2003-10-11 Shijun Liao
Multi-level adaptive solutions to boundary-value problems 1977-01-01 Achi Brandt
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Numerical Initial Value Problems in Ordinary Differential Equations 1973-07-01 E. I. C. W. Gear
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New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection–Diffusion Equations 2000-05-01 Alexander Kurganov Eitan Tadmor
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A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type 1947-01-01 J Crank P. Nicolson
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Difference Methods for Initial-Value Problems 1968-04-01 E. I. Robert D. Richtmyer K. W. Morton
Numerical Initial Value Problems in Ordinary Differential Equations 1972-05-01 James Watt
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LINEAR AND QUASILINEAR ELLIPTIC EQUATIONS 1969-11-01 D. E. Edmunds
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Dynamic Equations on Time Scales 2001-01-01 Martin Böhner Allan Peterson
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<i>Difference Methods for Initial-Value Problems</i> 1959-04-01 Robert D. Richtmyer E. H. Dill
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Quelques méthodes de résolution des problèmes aux limites non linéaires 1969-01-01 Jacques Louis Lions
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Numerical Solution of Partial Differential Equations, Finite Difference Methods. 1987-04-01 V. T. G. D. Smith
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On the Partial Difference Equations of Mathematical Physics 1967-03-01 Richard Courant Kurt Friedrichs Hans Lewy
Tables of integral transforms 1954-06-01
Elliptic Partial Differential Equations of Second Order 1977-01-01 David Gilbarg Neil S. Trudinger
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Differential Equations with Discontinuous Righthand Sides 1988-01-01 Alexander Filippov
Differential-Difference Equations 1963-01-01
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Non-Homogeneous Boundary Value Problems and Applications 1972-01-01 J. L. Lions Enrico Magenes
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Impulsive Differential Equations 1995-08-01 А. М. Самойленко N. A. Perestyuk

Most Recent Works

Action Title Date Authors
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Numerical approximation for singularly perturbed differential equations exhibiting significant positive shift arising in neuronal activity 2025-05-01 Akhila Mariya Regal Dinesh Kumar S
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Computational Methods, Existence and Uniqueness for Solving 2-D Fractional Nonlinear Fredholm Integro-Differential Equation 2025-05-01 A. M. Al‐Bugami Nuha Al‐Harbi A. M. S. Mahdy
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Convergence Analysis of Multi-Step Collocation Method to First-Order Volterra Integro-Differential Equation with Non-Vanishing Delay 2025-05-01 Ahmet Ali Eashel S. Pishbin Parviz Darania
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Numerical solution of fractional order Bagley-Torvik equation via Hermite wavelet method 2025-05-02 Muhammad Yousaf Aman Ullah Salman Zeb Umar Farooq Kamal Shah
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An adaptive scheme based on the cubic B-Spline collocation technique for time-fractional singular parabolic problems with semilinearity 2025-05-02 Bappa Ghosh Jugal Mohapatra
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Numerical algorithm for solving third-order Emden–Fowler type pantograph differential equations: Taylor operational matrix method 2025-05-02 Nikita Saha Randhir Singh
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On the influence of some absorption terms on the solutions of nonlinear parabolic equations 2025-05-02 Maria Michaela Porzio
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Fractional differentiation method: Application to the trapping reactions in the comb-like structures with relaxation 2025-05-02 Sergey D. Traytak
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Unique Solution Analysis for Generalized Caputo-Type Fractional BVP via Banach Contraction 2025-05-02 Zouaoui Bekri Sarah Aljohani Mohammad Esmael Samei Ali Akg ̈ul Abdelkader Belhenniche Ahmad Aloqaily Nabil Mlaiki
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A hybrid technique for approximating the solution of fractional order partial integro-differential equations 2025-05-02 Ahmed K. Mohsin Fajir A. Abdulkhaleq Osama H. Mohammed
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A robust Morley type conforming discontinuous galerkin method for a fourth order singular perturbation problem 2025-05-01 Yuping Zeng Shangyou Zhang
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Efficient Numerical Methods for Reaction–Diffusion Problems Governed by Singularly Perturbed Fredholm Integro-Differential Equations 2025-05-04 Sekar Elango L. Govindarao Muath Awadalla Hajer Zaway
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Evaluation of solutions of one class of finite-dimensional nonlinear equations. II 2025-05-05 B. D. Koshanov М. Отелбаев Abduhali Shynybekov
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Perturbed Caputo fractional Moreau’s sweeping process: existence, uniqueness, and numerical simulations 2025-05-05 Maria Ihsane El Bahi Zakaria Faiz Hicham Benaissa J. Vanterler da C. Sousa K. Hilal
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Spectral criteria for the asymptotic constancy of solutions to implicit difference equations 2025-05-05 Xuan‐Quang Bui Vu Trong Luong Nguyen Duong Toan Nguyen Ngoc Vien
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Asymptotic boundary behavior of large solutions to equations involving infinity Laplacian 2025-05-05 Ling Mi Yuan Yue
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Analyticity in space-time of solutions to evolution equations with multilinear operators based on maximal regularity 2025-05-05 K. Noda
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A non-uniform time-stepping method for time-fractional diffusion-wave equations with variable coefficients arising in fluid flow problems 2025-05-05 R. Burman Rajesh K. Pandey Sarita Kumari
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A hybrid numerical treatment of time-dependent convection dominated diffusion problems with integral boundary condition and large spatial delay 2025-05-05 Pratima Rai Amit Sharma
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Third-Order Sectorially A-Stable Alternating Implicit Runge–Kutta Schemes 2025-05-05 Alexandre Ern Jean‐Luc Guermond
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Unconditionally maximum bound principle preserving and energy stable finite element method for the Allen–Cahn equation with dynamic boundary condition 2025-05-06 Jiayin Li Jingwei Li
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The pricing of forward start options under jump diffusion model with stochastic interest rate and stochastic volatility 2025-05-06 Ruizhe Zhang Cuixiang Li Huili Liu
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Self-Similar Algebraic Spiral Solution of 2-D Incompressible Euler Equations 2025-05-06 Feng Shao Dongyi Wei Zhifei Zhang
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Superconvergence analysis for the Crank-Nicolson scheme of the Poisson-Nernst-Planck systems 2025-05-06 Minghao Li Minghao Li Z. X. Wu M M. Wang Liuchao Xiao
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An ESCA algorithm for solving the coefficient inverse problem of singularly perturbed parabolic convection–diffusion equation 2025-05-06 Li‐Bin Liu Tian Zhou Ling Li Xiongfa Mai Delong Guo
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Monotonic and oscillatory features of solutions to general functional differential equations with a neutral-delay argument 2025-05-06 Osama Moaaz Asma Al-Jaser
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Low-order efficient Adams–Bashforth–Moulton methods for first-order IVPs with oscillating solutions 2025-05-06 Chia‐Liang Lin Theodore E. Simos
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Robust Analysis of Perturbed Backward Doubly Stochastic Differential Equations 2025-05-06 Jasmina Đorđević
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Homoclinic Bifurcation from Perturbing a Cubic Integrable and Non-Hamiltonian System 2025-05-06 Qian Wen Wentao Huang Xianbo Sun
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Monotonicity of Limit Wave Speed in the pgKdV Equation with Nonlinear Terms of Arbitrarily High Degrees 2025-05-06 Ting An Yanfei Dai
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Stabilisation of the Landau-Lifshitz-Gilbert equation for numerical solution via standard methods 2025-05-06 A. E. Botha
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Efficient solution of one-dimensional time-dependent partial differential equations using a multi-step block method combined with compact finite difference schemes 2025-05-06 Akansha Mehta Gurjinder Singh Higinio Ramos
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Fractional neutral integro-differential dynamical systems with periodic BVPs 2025-05-07 Selvi Sellappan Emimal Navajothiai
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Modeling and analysis of the dynamics of an excessive gambling problem with modified fractional operator 2025-05-05 Mulualem Aychluh D. L. Suthar Clemente Cesarano Sunıl Dutt Purohıt
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Discretization of the Caputo time-fractional advection-diffusion problems with certain wavelet basis function 2025-05-07 Daniel Chinedu Iweobodo Godspower C. Abanum Ozioma Ogoegbulem Napoleon Ochonogor I.N. Njoseh
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Qualitative analysis for k-fractional integral boundary value problems of quasilinear equation with p-Laplacian operator 2025-05-07 Bo Zhang Xiaohui Shen Tengfei Shen
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Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted <i>L</i> <sup>∞</sup> spaces 2025-05-07 Ioakeim Ampatzoglou Joseph K. Miller Nataša Pavlović Maja Tasković
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A study on solvability and an iterative method for infinite systems of fractional integro-differential equations 2025-05-07 Rahul Rahul Sukanta Halder Manochehr Kazemi Mohammad Esmael Samei
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New qualitative results to a kind of non-autonomous third-order neutral delay differential equations 2025-05-04 Soliman A. Mahmoud
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Fractal Self‐Adjoint Higher Order Boundary‐Value Problems 2025-05-07 Bilender P. Allahverdiev Hüseyin Tuna
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Existence of multiple weak solutions for a class of fractional boundary value problems with Laplace operator 2025-05-08 Pu Wang
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A new energy dissipation-preserving Crank-Nicolson type nonconforming FEM for damped wave equation with cubic nonlinearity 2025-05-09 Dongyang Shi Xuemiao Xu
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Analysis of Iterative Method for Impulsive Neutral Functional Integro-Differential Equation Using Degree Theory 2025-05-08
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Spectral Stability of Contact Defects on Large Bounded Domains 2025-05-09 Milen Ivanov Björn Sandstede
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A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries 2025-05-09 Chuan Li Shan Zhao Benjamin Pentecost Yiming Ren Zhen Guan
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Homotopy Perturbation &lt;i&gt;ρ&lt;/i&gt;-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations 2025-05-09 Hamza Mihoubi Awatif Muflih Alqahtani Yacine Arioua Brahim Bouderah Tahar Tayebi
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Numerical Solutions of Time-Fractional N-W-S and Burger’s Equations Using the Tarig Projected Differential Transform Method (TPDTM) 2025-05-09 K Athira D Narasimhulu P. S. Brahmanandam
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Convergence and Stability Analysis of Galerkin Finite Element Method for Telegragh Equation with Piecewise Continuous Arguments 2025-05-09 Yongtang Chen Zhoushun Zheng
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Approximate Solution of the Nonlinear Buckmaster Partial Differential Equation using Exponential Fourth-order Differentiable Functions 2025-05-09 Usman Mohammed Yusuf Moses Anayo Mbah Collins E. Akpan Abubakar Abdulkarim María Jesús Teixidor de Otto Aminu Buhari Godwin Ma'aji Philip Nwanosike
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Application of the Tanh–Coth and HSI methods in deriving exact analytical solutions for the STFKS equation 2025-05-09 Abaker A. Hassaballa Elzain A. E. Gumma Ahmed M. A. Adam Omer M. A. Hamed Ali Satty Mohyaldein Salih Faroug A. Abdalla Zakariya M. S. Mohammed