×

Higher order methods for solving Volterra integrodifferential equations of the first kind. (English) Zbl 0810.65140

An integration by parts formula is applied to convert the Volterra integro-differential equation of the first kind into an equation of the second kind. Then a highly accurate diagonally implicit Runge-Kutta method is used for the numerical solution of the resulting equation. Finally, a numerical example is discussed to test the performance of the numerical method.
Reviewer: A.K.Pani (Bombay)

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Brunner, H.; van der Houwen, P. J., The Numerical Solution of Volterra Equations (1986), North-Holland: North-Holland Amsterdam · Zbl 0611.65092
[2] Linz, P., A simple approximation method for solving Volterra integrodifferential equations of the first kind, J. Inst. Math. Appl., 14, 211-215 (1974) · Zbl 0286.65058
[3] Linz, P., Analytical and Numerical Methods for Volterra Equations, (Siam Studies in Applied Mathematics (1985), SIAM) · Zbl 0193.13701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.