Experiments with a local adaptive grid \(h\)-refinement for the finite-difference solution of BVPs in singularly perturbed second-order ODEs

DOI10.1016/j.amc.2007.04.079zbMath1130.65072OpenAlexW2085989126MaRDI QIDQ2467415

Lesław K. Bieniasz

Publication date: 21 January 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.04.079

zbMATH Keywords

singular perturbationnumerical examplesboundary value problemsfinite-difference methodsadaptive gridsa posteriori error estimationconvection-reaction-diffusion

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (5)

A brief survey on numerical methods for solving singularly perturbed problems ⋮ Curved beam elasticity theory based on the displacement function method using a finite difference scheme ⋮ A set of compact finite-difference approximations to first and second derivatives, related to the extended Numerov method of Chawla on nonuniform grids ⋮ Adaptive solution of BVPs in singularly perturbed second-order ODEs, by the extended Numerov method combined with an iterative local grid \(h\)-refinement ⋮ Computational analysis of elastic field of deep curved beams/rings using displacement-function equilibrium method

Uses Software

• PDEX1M
• ORESD
• FDEM

Cites Work

• Adaptive refinement with truncation error injection
• A posteriori error estimates in finite difference techniques
• A comparison of some global methods for solving two-point boundary value problems
• An adaptive local mesh refinement method for time-dependent partial differential equations
• Asymptotic and numerical analysis of singular perturbation problems: A survey
• The principle of the difference of difference quotients as a key to the self-adaptive solution of nonlinear partial differential equations
• An adaptive Rothe method for nonlinear reaction-diffusion systems
• Analysis of local uniform grid refinement
• FDEM: How we make the FDM more flexible than the FEM
• Variational grid adaptation based on the minimization of local truncation error: Time-inde\-pend\-ent problems.
• Some aspects of adaptive grid technology related to boundary and interior layers.
• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• Singularly perturbed problems in partial differential equations: A survey
• Computational solution of two-dimensional unsteady PDEs using moving mesh methods
• About the central difference method for singularly perturbed boundary value problems
• A fully adaptive MOL-treatment of parabolic 1-D problems with extrapolation techniques
• Adaptive refinement for convection-diffusion problems based on a defect-correction technique and finite difference method
• A recipe to detect the error in discretization schemes
• An optimal control approach to a posteriori error estimation in finite element methods
• Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
• An Adaptive Method for Linear Parabolic Differential Equations
• Global Error Estimation in the Method of Lines for Parabolic Equations
• Adaptive refinement procedure for the finite difference method
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• On Non‐Linear Ordinary Differential Equations of Boundary Layer Type
• On a Differential Equation of Boundary Layer Type
• On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
• How we solve PDEs
• Goal-oriented error estimation and adaptivity for the finite element method
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