High order fitted operator numerical method for self-adjoint singular perturbation problems

DOI10.1016/j.amc.2005.01.069zbMath1086.65079OpenAlexW1971565872MaRDI QIDQ814747

Kailash C. Patidar

Publication date: 7 February 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.01.069

zbMATH Keywords

singular perturbationboundary value problemserror boundexponentially fitted difference scheme, Numerov's method

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (20)

A parallel approach for self-adjoint singular perturbation problems using Numerov's scheme ⋮ High order parameter uniform numerical method for singular perturbation problems ⋮ Limitations of Richardson's extrapolation for a high order fitted mesh method for self-adjoint singularly perturbed problems ⋮ \(\epsilon\) -uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddes ⋮ A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation ⋮ Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model ⋮ An equidistributed grid-based second-order scheme for a singularly perturbed Fredholm integro-differential equation with an interior layer ⋮ A numerical scheme for semilinear singularly perturbed reaction-diffusion problems ⋮ A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem ⋮ A robust fitted operator finite difference method for a two-parameter singular perturbation problem¹ ⋮ A novel method for singularly perturbed delay differential equations of reaction-diffusion type ⋮ On Richardson extrapolation for fitted operator finite difference methods ⋮ A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation ⋮ Unnamed Item ⋮ High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems ⋮ A recent survey on computational techniques for solving singularly perturbed boundary value problems ⋮ A robust fitted numerical method for singularly perturbed turning point problems whose solution exhibits an interior layer ⋮ A hybrid method for singularly perturbed convection-diffusion equation

Cites Work

• Perturbation methods in applied mathematics
• Singular perturbation methods for ordinary differential equations
• A lower bound for the smallest singular value of a matrix
• Global uniformly convergent schemes for a singularly perturbed boundary- value problem using patched base spline-functions
• A uniformly accurate spline collocation method for a singular perturbation problem
• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• Singularly perturbed problems in partial differential equations: A survey
• Multiple scale and singular perturbation methods
• Nonlinear singular perturbation phenomena: theory and applications
• A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions
• Perturbation methods and non-linear hyperbolic waves
• A variational difference scheme for a boundary value problem with a small parameter in the highest derivative
• On a Finite Difference Analogue of an Elliptic Boundary Problem which is Neither Diagonally Dominant Nor of Non‐negative Type
• Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
• RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: High order fitted operator numerical method for self-adjoint singular perturbation problems