Some implicit fourth and fifth order methods with optimum processes for numerical initial value problems

DOI10.2977/PRIMS/1195179624zbMath0601.65059OpenAlexW2032210104MaRDI QIDQ1081284

Masaharu Nakashima

Publication date: 1985

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195179624

zbMATH Keywords

numerical testsNewton iterationorderlocal truncation errorimplicit Runge-Kuttalocal accuracyA-stable Cash-Moore methodL-stable Cash method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Cites Work

• Implicit pseudo-Runge-Kutta processes
• High order methods for the numerical solution of two-point boundary value problems
• On pseudo-Runge-Kutta methods with 2 and 3 stages
• On a pseudo-Runge-Kutta method of order 6
• On the Solution of Block Tridiagonal Systems of Linear Algebraic Equations Having a Special Structure
• A high order method for the numerical solution of two-point boundary value problems
• A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations
• Coefficients for the study of Runge-Kutta integration processes

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