Runge-Kutta type integration formulas including the evaluation of the second derivative. I

DOI10.2977/prims/1195184026zbMath0529.65042OpenAlexW2001026955MaRDI QIDQ787647

Taketomo Mitsui

Publication date: 1982

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/1195184026

zbMATH Keywords

Runge-Kutta methodsone-step methodssecond derivative(p,q)-stage formulas

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (10)

Pseudo Runge-Kutta processes ⋮ Explicit strong stability preserving multistage two-derivative time-stepping schemes ⋮ Second derivative of high-order accuracy methods for the numerical integration of stiff initial value problems ⋮ Unnamed Item ⋮ Accuracy and Efficiency in Fixed-Point Neural ODE Solvers ⋮ Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes ⋮ High-order multiderivative time integrators for hyperbolic conservation laws ⋮ Two-step second-derivative high-order methods with two off-step points for solution of stiff systems ⋮ A strong stability preserving analysis for explicit multistage two-derivative time-stepping schemes based on Taylor series conditions ⋮ The efficiency of second derivative multistep methods for the numerical integration of stiff systems

Uses Software

• REDUCE

Cites Work

• Unnamed Item
• Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
• High order methods for the numerical integration of ordinary differential equations
• On one-step methods utilizing the second derivative
• On explicit one-step methods utilizing the second derivative
• An implicit one-step method of high-order accuracy for the numerical integration of ordinary differential equations
• Some general implicit processes for the numerical solution of differential equations
• Coefficients for the study of Runge-Kutta integration processes
• On Runge-Kutta processes of high order
• Implicit Runge-Kutta Processes
• Derivatives of composite functions

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