Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
This article studies optimal convergence of implicit Runge-Kutta methods (of Pouzet type) when applied to abstract Volterra integro-differential equations (including parabolic Volterra integro-partial differential equations). The problem is transformed into a differential equation in an appropriate function space. Since Runge-Kutta methods are invariant under this transformation, optimal convergence results can be obtained from \textit{C. Lubich} and \textit{A. Ostermann} [Runge-Kutta approximation of quasi-linear parabolic equations, Math. Comput. 64, No. 210, 601-627 (1995)]. Numerical examples are included.
abstract Volterra integro-differential equations
parabolic Volterra integro-partial differential equations
scientific article; zbMATH DE number 808205
scientific article