The numerical analysis of implicit Runge-Kutta methods for a certain nonlinear integro-differential equation

Authors:
Wei Yuan and Tao Tang

Journal:
Math. Comp. **54** (1990), 155-168

MSC:
Primary 65R20

MathSciNet review:
979942

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Abstract: In this paper and in an earlier 1987 paper, the mathematical theory and numerical methods for the nonlinear integro-differential equation

*m*stages for the approximate solution of the model equation was introduced. In this paper, we give a further numerical analysis of these methods. It is proved that the implicit Runge-Kutta methods with

*n*stages are of optimal approximation order . Some computational examples are given.

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DOI:
https://doi.org/10.1090/S0025-5718-1990-0979942-6

Article copyright:
© Copyright 1990
American Mathematical Society