Numerical treatment of singularly perturbed turning point problems with delay in time

Authors: Singh, Satpal, Kumar, Devendra, Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:1035-1064

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Shishkin mesh, Stability and convergence of numerical methods for boundary value problems involving PDEs, turning point, time lag, Spline approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, parameter-uniform convergence, Second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for ordinary differential equations, delay differential equation, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, splines, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, singular perturbation, Singular perturbations in context of PDEs

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Access URL: https://zbmath.org/8018422
https://doi.org/10.1007/s10910-025-01707-y

An Upwind-Block-Centered Multistep Difference Method for a Semiconductor Device and Numerical Analysis: An upwind-block-centered multistep difference method for a semiconductor device and numerical analysis

Authors: Yuan, Yirang, Li, Changfeng, Song, Huailing

Source: Advances in Applied Mathematics and Mechanics. 17:706-731

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Statistical mechanics of semiconductors, Finite difference methods for initial value and initial-boundary value problems involving PDEs, numerical computation, local conservation of mass, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, upwind block-centered multistep difference, three-dimensional semiconductor device, convergence analysis

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The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation: The spatial-temporal fourth-order conservative characteristic Runge-Kutta finite difference method for convection-dominated diffusion equation

Authors: Qin, Dan, Fu, Kai, Liang, Dong

Source: Advances in Applied Mathematics and Mechanics. 17:732-757

Subject Terms: Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, Finite difference methods for boundary value problems involving PDEs, spatial-temporal fourth-order, mass conservation, convection-dominated diffusion equations, characteristic method

File Description: application/xml

Access URL: https://zbmath.org/8033900
https://doi.org/10.4208/aamm.oa-2023-0173

Approximating and Preconditioning the Stiffness Matrix in the GoFD Approximation of the Fractional Laplacian: Approximating and preconditioning the stiffness matrix in the GoFD approximation of the fractional Laplacian

Authors: Huang, Weizhang, Shen, Jinye

Source: Communications in Computational Physics. 37:1-29

Subject Terms: Finite difference methods for boundary value problems involving PDEs, overlay grid, preconditioning, FOS: Mathematics, fractional Laplacian, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Fractional partial differential equations, finite difference approximation, stiffness matrix, 65N06, 35R11

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Access URL: http://arxiv.org/abs/2407.07199
https://zbmath.org/8013530
https://doi.org/10.4208/cicp.oa-2024-0079

A Fast Offline/Online Forward Solver for Stationary Transport Equation with Multiple Inflow Boundary Conditions and Varying Coefficients: A fast offline/online forward solver for stationary transport equation with multiple inflow boundary conditions and varying coefficients

Authors: Fu, Jingyi, Tang, Min

Source: Communications in Computational Physics. 37:457-497

Subject Terms: Finite difference methods for boundary value problems involving PDEs, radiative transport equation, offline/online decomposition, Boundary-layer theory for compressible fluids and gas dynamics, PDEs in connection with mechanics of particles and systems of particles, tailored finite point method, Mathematics - Numerical Analysis, asymptotic preserving, boundary/interface layer

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Access URL: http://arxiv.org/abs/2401.03147
https://zbmath.org/8033883
https://doi.org/10.4208/cicp.oa-2022-0127

THE EXISTENCE OF THE GLOBAL SOLUTION OF THE SEMI-LINEAR SCHRÖDINGER EQUATION WITH NUMERICAL COMPUTATION ON THE DIRICHLET BOUNDARY: The existence of the global solution of the semi-linear Schrödinger equation with numerical computation on the Dirichlet boundary

Authors: Chin, Pius W. M.

Source: Journal of Applied Analysis & Computation. 15:786-809

Subject Terms: Finite difference methods for boundary value problems involving PDEs, semilinear equation, nonstandard finite difference method, Error bounds for boundary value problems involving PDEs, Semilinear elliptic equations, Schrödinger equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Galerkin method, optimal rate of convergence

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A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces: A meshfree RBF-FD constant along normal method for solving PDEs on surfaces

Authors: Víctor Bayona, Argyrios Petras, Cécile Piret, Steven J. Ruuth

Contributors: Comunidad de Madrid

Source: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Matemáticas, Closest point method, Meshfree, Numerical Analysis (math.NA), meshfree, Numerical differentiation, Approximation by polynomials, Spline approximation, High-order methods, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, high-order methods, PDEs on surfaces, FOS: Mathematics, RBF-FD, Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Interpolation in approximation theory, Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs, closest point method

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2412.14761
https://hdl.handle.net/10016/46963

New Time Domain Decomposition Methods for Parabolic Optimal Control Problems II: Neumann–Neumann Algorithms: New time domain decomposition methods for parabolic optimal control problems. II: Neumann-Neumann algorithms

Authors: Martin J. Gander, Liu-Di Lu

Source: SIAM Journal on Numerical Analysis. 62:2588-2610

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Controllability, parallel in time, time domain decomposition, 65M12, 65M55, 65Y05, Parallel numerical computation, parabolic optimal control problems, Numerical Analysis (math.NA), PDE constrained optimization (numerical aspects), 01 natural sciences, convergence analysis, Neumann-Neumann algorithm, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Optimization and Control (math.OC), Approximation by arbitrary linear expressions, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2401.15522
https://zbmath.org/7957568
https://doi.org/10.1137/24m1634424

A Robust and higher order numerical technique for a time-fractional equation with nonlocal condition: A robust and higher order numerical technique for a time-fractional equation with nonlocal condition

Authors: Taneja, Komal, Deswal, Komal, Kumar, Devendra, Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:626-649

Subject Terms: Finite difference methods for boundary value problems involving PDEs, matrix stability, Caputo's derivative, Fractional derivatives and integrals, nonlocal condition, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Direct numerical methods for linear systems and matrix inversion, Fractional partial differential equations, time-fractional reaction-advection-diffusion equation, modified Gauss elimination

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A parameter uniform numerical method for 2D singularly perturbed elliptic differential-difference equations

Authors: null Garima, Komal Bansal, Kapil K. Sharma

Source: Journal of Applied Mathematics and Computing. 70:6347-6372

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Error bounds for boundary value problems involving PDEs, space shift, differential-difference equation, Numerical computation of solutions to systems of equations, singularly perturbed problem, convection-diffusion problem, Stability and convergence of numerical methods for boundary value problems involving PDEs, 2D elliptic equation, non standard finite difference method

File Description: application/xml

Access URL: https://zbmath.org/8036706
https://doi.org/10.1007/s12190-024-02203-3

A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model: A two-level Crank-Nicolson difference scheme and its Richardson extrapolation methods for a magneto-thermo-elasticity model

Authors: Deng, Dingwen, Zhang, Ruyu

Source: Advances in Applied Mathematics and Mechanics. 16:608-635

Subject Terms: Finite difference methods for boundary value problems involving PDEs, energy conservation, Iterative numerical methods for linear systems, Extrapolation to the limit, deferred corrections, convergence, Richardson extrapolation methods, priori estimation, Symbolic computation and algebraic computation, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Electromagnetic effects in solid mechanics, Classical linear elasticity, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, finite difference method, solvability

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On the Monotonicity of $Q^3$ Spectral Element Method for Laplacian: On the monotonicity of \(Q^3\) spectral element method for Laplacian

Authors: Cross, Logan J., Zhang, Xiangxiong

Source: Annals of Applied Mathematics. 40:161-190

Subject Terms: Finite difference methods for boundary value problems involving PDEs, inverse positivity, discrete maximum principle, spectral element method, high order accuracy, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, discrete Laplacian, monotonicity

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Meshfree Finite Difference Solution of Homogeneous Dirichlet Problems of the Fractional Laplacian: Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian

Authors: Jinye Shen, Bowen Shi, Weizhang Huang

Source: Communications on Applied Mathematics and Computation. 7:589-605

Subject Terms: Finite difference methods for boundary value problems involving PDEs, overlay grid, FOS: Mathematics, arbitrary domain, fractional Laplacian, finite difference (FD), Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Fractional partial differential equations, 65N06, 35R11, meshfree

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.04407

A family of linearly weighted-$$\theta $$ compact ADI schemes for sine-Gordon equations in high dimensions: A family of linearly weighted-\( \theta\) compact ADI schemes for sine-Gordon equations in high dimensions

Authors: Zhang, Qifeng, Li, Dongfang, Mao, Wanying

Source: Numerical Algorithms. 98:797-838

Subject Terms: Finite difference methods for boundary value problems involving PDEs, sine-Gordon equation, convergence, KdV equations (Korteweg-de Vries equations), Finite difference methods for initial value and initial-boundary value problems involving PDEs, compact ADI scheme, stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, weighted-\( \theta\) scheme

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The second-order modified upwind PPM characteristic difference method and analysis for solving convection-diffusion equations

Authors: Ren, Huimin, Zhang, Qi, Zhou, Zhongguo

Source: Numerical Algorithms. 98:503-530

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, PPM, Error bounds for initial value and initial-boundary value problems involving PDEs, convergence, characteristic difference, Finite difference methods for initial value and initial-boundary value problems involving PDEs, convection-diffusion equation, modified upwind, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability

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A Cole–Hopf Transformation Based Fourth-Order Multiple-Relaxation-Time Lattice Boltzmann Model for the Coupled Burgers’ Equations: A Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann model for the coupled Burgers' equations

Authors: Ying Chen, Xi Liu, Zhenhua Chai, Baochang Shi

Source: Journal of Scientific Computing. 103

Subject Terms: Finite difference methods for boundary value problems involving PDEs, multiple-relaxation-time lattice Boltzmann model, FOS: Mathematics, Particle methods and lattice-gas methods, \(d\)-dimensional coupled Burgers' equations, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for boundary value problems involving PDEs, Cole-Hopf transformation

File Description: application/xml

Access URL: http://arxiv.org/abs/2309.02825
https://zbmath.org/8022428
https://doi.org/10.1007/s10915-025-02844-x

A Simple and Efficient Finite Difference Method for the Tempered Nonlocal Laplacian: A simple and efficient finite difference method for the tempered nonlocal Laplacian

Authors: Xuehong Cui, Rui Du, Zhaopeng Hao

Source: Journal of Scientific Computing. 103

Subject Terms: Finite difference methods for boundary value problems involving PDEs, convergence, Fractional derivatives and integrals, fast algorithm, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability, Fractional partial differential equations, Numerical methods for discrete and fast Fourier transforms, tempered nonlocal Laplacian, finite difference method

File Description: application/xml

Access URL: https://zbmath.org/8016237
https://doi.org/10.1007/s10915-025-02823-2

Stability and Accuracy of a Meshless Finite Difference Method for the Stokes Equations: Stability and accuracy of a meshless finite difference method for the Stokes equations

Authors: Alexander Westermann, Oleg Davydov, Andriy Sokolov, Stefan Turek

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Finite difference methods for boundary value problems involving PDEs, convergence rate, optimal stability, driven cavity flow, Moffatt eddy, Stability and convergence of numerical methods for boundary value problems involving PDEs, radial basis function, Finite difference methods applied to problems in fluid mechanics, Stokes and related (Oseen, etc.) flows

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A New Type of Increasingly Higher Order of Finite Difference Ghost Multi-resolution WENO Schemes for Hamilton-Jacobi Equations: A new type of increasingly higher order of finite difference ghost multi-resolution WENO schemes for Hamilton-Jacobi equations

Authors: Yan Zhang, Jun Zhu

Source: Journal of Scientific Computing. 102

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), ghost multi-resolution WENO scheme, finite difference, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, orthogonal Legendre basis, Hamilton-Jacobi equations

File Description: application/xml

Access URL: https://zbmath.org/7975327
https://doi.org/10.1007/s10915-025-02787-3

A Grid-Overlay Finite Difference Method for Inhomogeneous Dirichlet Problems of the Fractional Laplacian on Arbitrary Bounded Domains: A grid-overlay finite difference method for inhomogeneous Dirichlet problems of the fractional Laplacian on arbitrary bounded domains

Authors: Weizhang Huang, Jinye Shen

Source: Journal of Scientific Computing. 102

Subject Terms: Finite difference methods for boundary value problems involving PDEs, overlay grid, finite difference, mesh adaptation, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Fractional partial differential equations, Computational methods for sparse matrices, Error bounds for initial value and initial-boundary value problems involving PDEs, Fractional derivatives and integrals, inhomogeneous fractional Laplacian, Preconditioners for iterative methods, arbitrary domain, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7975323
https://doi.org/10.1007/s10915-024-02782-0