Diagonally implicit Runge-Kutta formulae for the numerical integration of nonlinear two-point boundary value problems

DOI10.1016/0898-1221(84)90043-9zbMath0565.34012OpenAlexW1998010299MaRDI QIDQ1058641

Jeff R. Cash

Publication date: 1984

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(84)90043-9

zbMATH Keywords

algorithmsmid-point ruleNumerical resultsRunge Kutta formulae

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for ordinary differential equations (65L99) Numerical analysis in abstract spaces (65J99)

Related Items (3)

Exponentially fitted symmetric and symplectic DIRK methods for oscillatory Hamiltonian systems ⋮ A spline-based method of solution of nonlinear two-point boundary-value problems ⋮ Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I

Cites Work

• A variable order deferred correction algorithm for the numerical solution of nonlinear two point boundary value problems
• High order methods for the numerical solution of two-point boundary value problems
• On the estimation of errors propagated in the numerical integration of ordinary differential equations
• The method of iterated defect-correction and its application to two-point boundary value problems. I
• Iterated defect correction for differential equations. I: Theoretical results
• On the Efficient Implementation of Implicit Runge-Kutta Methods
• Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations Part II. The Stiff Case
• Diagonally Implicit Runge-Kutta Formulae with Error Estimates
• A Theoretical Framework for Proving Accuracy Results for Deferred Corrections
• Semiexplicit A-Stable Runge-Kutta Methods
• On the implementation of implicit Runge-Kutta methods
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems
• The Application of Implicit Runge-Kutta and Collocation Methods to Boundary-Value Problems
• Coefficients for the study of Runge-Kutta integration processes

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