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Mathematics › Numerical Analysis

Numerical methods for differential equations

Works Count: 59451

Description

This cluster of papers focuses on the development and analysis of numerical integration methods for solving differential equations, with a particular emphasis on exponential integrators, symplectic methods, time-stepping schemes, and variational integrators. The research covers a wide range of applications including the numerical solution of the Schrödinger equation, Hamiltonian systems, and matrix exponential computations.

Keywords

Numerical Integration; Differential Equations; Exponential Integrators; Symplectic Methods; Time-Stepping Schemes; Variational Integrators; Matrix Exponential; Runge-Kutta Methods; Schrödinger Equation; Hamiltonian Systems

Most Cited Works

Action Title Date Authors
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Functional Analysis and Semi-groups 1996-02-06 Einar Hille Robert A. Phillips
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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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Interpolation of Operators 1988-01-01 Curtis D. Bennett M Sharpley
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Stability of Time-Delay Systems 2003-01-01 Keqin Gu Vladimir L. Kharitonov Jie Chen
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Theory and applications of Hopf bifurcation 1981-01-01 Brian Hassard Nicholas D. Kazarinoff Yujie Wan
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The analysis of linear partial differential operators 1990-01-01 Lars Hörmander
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An Introduction to Infinite-Dimensional Linear Systems Theory 1995-01-01 Ruth F. Curtain Hans Zwart
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Solving Frontier Problems of Physics: The Decomposition Method 1994-01-01 George Adomian
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Applications of lie groups to differential equations 1990-09-01 Peter J. Olver
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Stochastic Stability of Differential Equations 2011-09-19 R. Z. Khas’minskiĭ
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Theory and Applications of Fractional Differential Equations 2006-01-01 Anatoly A. Kilbas H. M. Srivastava Juan J. Trujillo
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Elements of Applied Bifurcation Theory 2004-01-01 Yuri A. Kuznetsov
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Partial Differential Equations 2010-03-02 Lawrence Evans
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Elliptic Partial Differential Equations of Second Order 2001-01-01 David Gilbarg Neil S. Trudinger
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Analysis of Fractional Differential Equations 2002-01-01 Kai Diethelm Neville J. Ford
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Differential Equations, Dynamical Systems, and Linear Algebra 1974-01-01 Morris W. Hirsch Stephen T. Smale
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Some methods of speeding up the convergence of iteration methods 1964-01-01 B. T. Polyak
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Solving Ordinary Differential Equations II 1996-01-01 Ernst Hairer Gerhard Wanner
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On the Stability of the Linear Functional Equation 1941-04-15 D. H. Hyers
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An Introduction to Numerical Analysis 1990-04-01 F. S. Kendall Atkinson
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DIFFERENTIAL-DIFFERENCE EQUATIONS 1987-02-01 Kenneth L. Cooke
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Reversible multiple time scale molecular dynamics 1992-08-01 Mark E. Tuckerman B. J. Berne Glenn Martyna
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Applied Numerical Methods 1970-07-01 Donald Greenspan Brice Carnahan H. Luther James Wilkes
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A Numerical Method for Solving Incompressible Viscous Flow Problems 1997-08-01 Alexandre J. Chorin
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Linear Partial Differential Operators 1963-01-01 Lars Hörmander
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State-space solutions to standard H/sub 2/ and H/sub infinity / control problems 1989-01-01 John C. Doyle K. Glover Pramod P. Khargonekar Bruce A. Francis
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Solving ordinary differential equations I. nonstiff problems 1987-10-01 Ernst Hairer Syvert P. Nørsett Gerhard Wanner
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Maximum Principles in Differential Equations 1984-01-01 Murray H. Protter Hans F. Weinberger
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P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation 2007-12-01 Berk Hess
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<i>Theory of Ordinary Differential Equations</i> 1956-02-01 Earl A. Coddington Norman Levinson T. Teichmann
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Theory of Functional Differential Equations 1977-01-01 Jack K. Hale
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New development in freefem++ 2012-01-01 Frédéric Hecht
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Strong Stability-Preserving High-Order Time Discretization Methods 2001-01-01 Sigal Gottlieb Chi‐Wang Shu Eitan Tadmor
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The MATLAB ODE Suite 1997-01-01 L. F. Shampine Mark W. Reichelt
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Geometrical Methods in the Theory of Ordinary Differential Equations 1988-01-01 V. I. Arnold
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Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems 2002-01-01 Douglas N. Arnold Franco Brezzi Bernardo Cockburn L. D. Marini
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A family of embedded Runge-Kutta formulae 1980-03-01 John R. Dormand P.J. Prince
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Group Analysis of Differential Equations. 1985-02-01 Willard Miller Л.В. Овсянников
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Numerical Initial Value Problems in Ordinary Differential Equations 1973-07-01 E. I. C. W. Gear
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SUNDIALS 2005-09-01 A.C. Hindmarsh Peter N. Brown Keith Eric Grant Steven L. Lee Radu Serban Dan Shumaker Carol S. Woodward
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Numerical Initial Value Problems in Ordinary Differential Equations 1972-05-01 James Watt
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Symmetries and Differential Equations 1989-01-01 George W. Bluman Sukeyuki Kumei
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Stochastic Differential Equations: Theory and Applications. 1976-01-01 P. Whittle Ludwig Arnold
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Ordinary Differential Equations 1945-10-01 A. T. Lonseth E. L. Ince
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Partial Differential Equations 1988-01-01 Shiing-Shen Chern
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Ordinary Differential Equations 2017-10-12 John M. Stewart
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Introduction to Functional Differential Equations 1993-01-01 Jack K. Hale Sjoerd M. Verduyn Lunel
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Applications of Lie Groups to Differential Equations 1986-01-01 Peter J. Olver
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Applications of Lie Groups to Differential Equations 1993-01-01 Peter J. Olver
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Differential Equations with Discontinuous Righthand Sides 1988-01-01 Alexander Filippov

Most Recent Works

Action Title Date Authors
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Overlapping Domain Decomposition Methods for Noncoercive Hamilton-Jacobi-Bellman Equation 2025-05-01 Samar Chebbah Mohamed Haiour Sofiane Madi
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Stability Analysis of Coupled Hadamard Hybrid Fractional Differential Equations with Generalized Hybrid Boundary Conditions 2025-05-01 Shahid Iqbal Usman Riaz Saeed Islam Syed Omar Shah Adnène Arbi
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On the Efficiency of a One-Fifth Step Hybrid Block Method for the Numerical Solution of Second-Order Ordinary Differential Equations 2025-05-01 Oluwasayo Esther Taiwo
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High-order WENO finite-difference methods for hyperbolic nonconservative systems of Partial Differential Equations 2025-05-01 Baifen Ren Carlos Parés
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Two minimal-variable symplectic integrators for stochastic spin systems 2025-05-02 Sagy Ephrati Erik Jansson
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Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions 2025-05-02 Maryam Mohseni Davood Rostamy
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Stability Analysis of Solutions to the Time–Fractional Nonlinear Schrödinger Equations 2025-05-02 Nazia Irshad Rahim Shah Kinza Liaquat Emad E. Mahmoud
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A Preconditioner for the Grad-Div Stabilized Equal-Order Finite Elements Discretizations of the Oseen Problem 2025-05-02 Yunhui He Maxim A. Olshanskii
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Thermodynamic analysis and mass spectra of heavy mesons via the generalized fractional Klein-Gordon equation 2025-05-01 M. Abu‐Shady Hamdi Fathallah
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APPLICATION OF THE SOME BLAISE ABBO METHOD (SBA) FOR SOLVING THE NONLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS 2025-05-02 Rashid Ali Gires Dimitri Nkaya Joseph Bonazebi Yindoula Massamba Alphonse
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Integration of Hamiltonian equations with two degrees of freedom for a truncated normal form at 2:1 resonance 2025-05-03 А. Г. Петров
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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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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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Optimization of semilinear higher-order delay differential inclusions 2025-05-05 Elimhan N. Mahmudov Dilara Mastaliyeva
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Multi-bump solutions for the double phase critical Schrödinger equations involving logarithmic nonlinearity 2025-05-05 Lifeng Guo Sihua Liang Bin Lin Patrizia Pucci
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Orthogonal polynomial-based neural network solution for differential equations with implicit boundary conditions 2025-05-05 Saikat Dey Shruti Dubey
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Analytic continuation of one variable power series by interpolating its coefficients 2025-05-05 Aleksandr Mkrtchyan
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Modified TASE Runge–Kutta Methods for Integrating Stiff Differential Equations 2025-05-05 Lidia Aceto Dajana Conte Giovanni Pagano
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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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Mixed Precision Orthogonalization-Free Projection Methods for Eigenvalue and Singular Value Problems 2025-05-01 Tianshi Xu Ziqi Zhang Jie Chen Yousef Saad Yuanzhe Xi
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Higher-Order Differential Correction Schemes for the Two-Point Boundary Value Problem 2025-05-06 Sharad Sharan Puneet Singla Roshan T. Eapen Robert G. Melton
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A Multistep Chebyshev Collocation Scheme for Fractional Differential Equations of Pantograph Type 2025-05-01 Changqing Yang Jianhua Hou Xiao-Guang Lv
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Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models 2025-05-06 Matteo Tomasetto Francesco Braghin Andrea Manzoni
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Efficient numerical methods based on general linear methods for Volterra integral equations 2025-05-01 Z. Ghahremani Ali Abdi Gholamreza Hojjati
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Numerical Solution of First and Higher Order IVPs Via a Single Continuous Block Method 2025-05-06 Jamiu Garba Khadeejah James Audu Umaru Mohammed Abd’gafar Tunde Tiamiyu
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On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy 2025-05-06 Dilveen M. Ahmed Bewar A. Mahmood Ahmad Alalyani
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Stiffness resilient exponential integrators and $$\varphi $$-order conditions 2025-05-06 Valentin Dallerit Mayya Tokman
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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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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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Stabilization of Linear Port-Hamiltonian Descriptor Systems via Output Feedback 2025-05-06 Delin Chu Volker Mehrmann
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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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Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system 2025-05-06 Jiao Zhang Fucai You
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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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Data-driven reduced-order models for port-Hamiltonian systems with operator inference 2025-05-07 Yuwei Geng Lili Ju Boris Krämer Zhu Wang
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Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach 2025-05-06 Mostafa Eslami
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New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System 2025-05-07 Feriel Boudersa Abdelaziz Mennouni Ravi P. Agarwal
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Time-Dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence 2025-05-07 Di Fang Diyi Liu Rahul Sarkar
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PERIODIC AND PSEUDO PERIODIC SOLUTIONS FOR MATRIX SYLVESTER DYNAMIC SYSTEM ON MEASURE CHAINS 2025-05-01 CH. Harisha B. V. Appa Rao A. Sreenivasulu
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Theoretical analysis and applications of fixed-point theorems in delay fractional differential equations 2025-05-07 Mohamed Balegh Ahmed Ghezal
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Introduction of fractional damping to nonlinear GE beam model 2025-05-07 Nobuyuki Shimizu Takeshi Fujikawa Masataka Fukunaga
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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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A posteriori error estimates and time adaptivity for fully discrete finite element method for the incompressible Navier-Stokes equations 2025-05-01 Shuo Yang Hongjiong Tian
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Energy preserving high order mimetic methods for hamiltonian equations 2025-05-01 S. Anand José E. Castillo
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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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An innovative low-order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1784" altimg="si15.svg"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-Galerkin mixed finite element framework for superconvergence analysis in nonlinear Klein–Gordon equations 2025-05-01 Yanmi Wu Xin Ge
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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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A New Coupled Subdiffusion Model and Its Partitioned Time-Stepping Algorithm 2025-05-01 Zheng Li Yuting Xiang Hui Xu J. 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