Stability analysis of the de Hoog and Weiss implicit Runge-Kutta methods for the Volterra integral and integrodifferential equations

DOI10.1016/0377-0427(90)90015-RzbMath0699.65089MaRDI QIDQ913473

Antonia Vecchio, Maria Rosaria Crisci, Elvira Russo

Publication date: 1990

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilitynumerical examplesspline collocation methodRunge-Kutta-type methodsVolterra integro- differential equations

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10)

Related Items

Multistep Runge-Kutta methods for Volterra integro-differential equations ⋮ Stability of \(\vartheta\)-methods for delay integro-differential equations. ⋮ Nonlinear stability of direct quadrature methods for Volterra integral equations ⋮ Stability of parallel Volterra-Runge-Kutta methods ⋮ Stability of collocation methods for Volterra integro-differential equations ⋮ Stability analysis of Runge-Kutta methods for Volterra integro-differential equations ⋮ Global stability analysis of the Runge-Kutta methods for Volterra integral and integro-differential equations with degenerate kernels

Cites Work

• Unnamed Item
• Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations
• On the stability of the one-step exact collocation methods for the numerical solution of the second kind Volterra integral equation
• Implicit Runge-Kutta methods for second kind Volterra integral equations
• Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations
• Regions of Stability in the Numerical Treatment of Volterra Integro-Differential Equations
• An Extension of the Eneström-Kakeya Theorem and Its Sharpness
• Convergence of a Block-by-Block Method for Nonlinear Volterra Integro-Differential Equations