Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

\begin{displaymath}\begin{array}{*{20}{c}} {u'(t) + p(t)u(t) + \int_0^t {k(t} ,s... ...\leq t \leq T,} \hfill \\ {u(0) = {u_0}} \hfill \\ \end{array} \end{displaymath}

are considered. Equations of this type occur as model equations for describing turbulent diffusion. Previously, the existence and uniqueness properties of the solutions of the model equation were solved completely, and a class of implicit Runge-Kutta methods with 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 $ p = 2m$. Some computational examples are given.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20

Retrieve articles in all journals with MSC: 65R20

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society