Interpolation Schemes for Collocation Solutions of Two-Point Boundary Value Problems

DOI10.1137/0907021zbMath0635.65098OpenAlexW2092563948MaRDI QIDQ3774879

Steven A. Pruess

Publication date: 1986

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0907021

zbMATH Keywords

stabilitycomparison of methodsnumerical examplesspline interpolationcollocationstorage requirementsasymptotic errorsoperation countsinterpolatory algorithmssuperconvergent meshpoint approximations

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (9)

Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems ⋮ Adams-Bashforth and Adams-Moulton methods for solving differential Riccati equations ⋮ Superconvergent interpolants for collocation methods applied to Volterra integro-differential equations with delay ⋮ Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants ⋮ Solving boundary value problems of ordinary differential equations with non-separated boundary conditions ⋮ Solving differential matrix Riccati equations by a piecewise-linearized method based on the conmutant equation ⋮ High-order interpolants for solutionsof two-point boundary value problems using MIRK methods ⋮ Stability bounds for local Lagrangian interpolation ⋮ Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems

Uses Software

• COLSYS

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