A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions

DOI10.1002/num.22931WikidataQ115397120 ScholiaQ115397120MaRDI QIDQ6064517

Aastha Gupta, Manju Sharma, Aditya Kaushik

Publication date: 12 December 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

singular perturbationinitial-boundary value problemsmesh generationgrid equidistributionhybrid difference schemeboundary valueparameter uniform methodsrobust discretization

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Related Items (1)

Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time

Cites Work

• Unnamed Item
• A robust adaptive grid method for a system of two singularly perturbed convection-diffusion equations with weak coupling
• Solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post-processing
• A uniformly convergent nonstandard finite difference scheme for a system of convection-diffusion equations
• Theory of exponential splines
• Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
• Numerical approach of Fokker-Planck equation with Caputo-Fabrizio fractional derivative using Ritz approximation
• Radial basis functions for solving differential equations: ill-conditioned matrices and numerical stability
• Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
• On supraconvergence phenomenon for second order centered finite differences on non-uniform grids
• A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms
• A new approach for solving multi variable orders differential equations with Mittag-Leffler kernel
• A higher-order hybrid finite difference method based on grid equidistribution for fourth-order singularly perturbed differential equations
• A new approach for solving integro-differential equations of variable order
• A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem
• Superconvergence of finite element method for singularly perturbed convection-diffusion equations in 1D
• A discrete Schwarz waveform relaxation method of higher order for singularly perturbed parabolic reaction-diffusion problems
• The parameter uniform numerical method for singularly perturbed parabolic reaction-diffusion problems on equidistributed grids
• Can VEGFC form Turing patterns in the zebrafish embryo?
• Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter
• Grid equidistribution for reaction-diffusion problems in one dimension
• A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems
• A robust spline difference method for Robin-type reaction-diffusion problem using grid equidistribution
• Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• Nonstandard finite difference methods: recent trends and further developments
• Convergence of de Boor's algorithm for the generation of equidistributing meshes
• A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem
• A difference scheme for a singularly perturbed parabolic equation with discontinuous coefficients and concentrated factors
• Smoothed particle hydrodynamics: theory and application to non-spherical stars
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
• Finite Volume Methods for Hyperbolic Problems
• Solving FDEs with Caputo‐Fabrizio derivative by operational matrix based on Genocchi polynomials
• Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems
• Mixed Finite Element Methods and Applications
• -uniform schemes with high-order time-accuracy for parabolic singular perturbation problems
• Parameter uniform approximations for time‐dependent reaction‐diffusion problems
• On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
• A minimal stabilisation procedure for mixed finite element methods
• A higher-order scheme for quasilinear boundary value problems with two small parameters

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