Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems

DOI10.1016/S0168-9274(98)00045-2zbMath0926.65078OpenAlexW2081208885MaRDI QIDQ1294523

R. W. Wright, Jeff R. Cash

Publication date: 29 June 1999

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(98)00045-2

zbMATH Keywords

singular perturbationnumerical examplesnonlinear two-point boundary value problemsinterpolating polynomialsimplicit Runge-Kutta formulaeuniform accuracydeferred correction schemes

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15)

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Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions, A two-stage LGSM for three-point BVPs of second-order ODEs, High-order interpolants for solutionsof two-point boundary value problems using MIRK methods, Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions., Disclinated states in nematic elastomers.

Uses Software

• COLSYS

Cites Work

• Unnamed Item
• A comparison of some global methods for solving two-point boundary value problems
• High order methods for the numerical solution of two-point boundary value problems
• An automatic continuation strategy for the solution of singularly perturbed linear two-point boundary value problems
• A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
• Interpolation Schemes for Collocation Solutions of Two-Point Boundary Value Problems
• 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
• Collocation Software for Boundary-Value ODEs
• A Theoretical Framework for Proving Accuracy Results for Deferred Corrections
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• Order Barriers and Characterizations for Continuous Mono-Implicit Runge- Kutta Schemes
• Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I
• A Stable High-Order Interpolation Scheme for Superconvergent Data
• An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems