Defect Correction for Two-Point Boundary Value Problems on Nonequidistant Meshes

DOI10.2307/2153443zbMath0828.65102OpenAlexW2002927493MaRDI QIDQ4846011

Robert D. Russell, Gerald Moore, Jeff R. Cash, John C. Butcher

Publication date: 10 January 1996

Full work available at URL: https://doi.org/10.2307/2153443

zbMATH Keywords

numerical resultsfinite difference methoddefect correctionhigher-order methodssupra-convergencesecond-order two-point boundary value problemvariable mesh spacing

Mathematics Subject Classification ID

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

Related Items

Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations ⋮ On the error estimation of spline method for second order boundary value problem ⋮ Runge-Kutta methods for the solution of stiff two-point boundary value problems ⋮ On the numerical approximation of trajectories in the phase plane ⋮ Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems

Uses Software

• PASVA3
• COLSYS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Explicit construction of an inertial manifold for a reaction diffusion equation
• Adaptive Runge-Kutta methods for nonlinear two-point boundary value problems with mild boundary layers
• Defect correction from a Galerkin viewpoint
• High order P-stable formulae for the numerical integration of periodic initial value problems
• High order methods for the numerical solution of two-point boundary value problems
• A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
• A Method for the Spatial Discretization of Parabolic Equations in One Space Variable
• Supra-Convergent Schemes on Irregular Grids
• The Numerical Solution of Second-Order Boundary Value Problems on Nonuniform Meshes
• Low-dimensional behaviour in the complex Ginzburg-Landau equation
• On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae
• Optimal Recovery in the Finite-Element Method, Part 2: Defect Correction for Ordinary Differential Equations
• Collocation Software for Boundary-Value ODEs
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• A Theoretical Framework for Proving Accuracy Results for Deferred Corrections
• A Variable Order Finite Difference Method for Nonlinear Multipoint Boundary Value Problems
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• A sixth order tridiagonal finite difference method for non-linear two-point boundary value problems
• Numerov’s Method with Deferred Corrections for Two-Point Boundary-Value Problems
• An eighth order tridiagonal finite difference method for nonlinear two-point boundary value problems
• Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I
• Difference Approximations for Boundary and Eigenvalue Problems for Ordinary Differential Equations