An Adaptive Boundary Value Runge–Kutta Solver for First Order Boundary Value Problems

DOI10.1137/0722008zbMath0569.65060OpenAlexW2087577099MaRDI QIDQ3685966

Suchitra Gupta

Publication date: 1985

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0722008

zbMATH Keywords

numerical examplesorder conditionsembedded methodsButcher groupgap schemeRunge- Kuttaadaptive finite difference solver

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)

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Efficient classes of Runge-Kutta methods for two-point boundary value problems ⋮ Relationships among some classes of implicit Runge-Kutta methods and their stability functions ⋮ New interpolants for asymptotically correct defect control of BVODEs ⋮ Runge-Kutta methods for the solution of stiff two-point boundary value problems ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ A note on error expressions for reflected and averaged implicit Runge- Kutta methods ⋮ Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I ⋮ On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods ⋮ Multiderivative Runge-Kutta processes for two-point boundary value problems

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