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A GLMs-based difference-quadrature scheme for Volterra integro-differential equations. (English) Zbl 1464.65072

Summary: In this paper, a class of general linear methods is combined with a special quadrature rule inherited from natural Runge-Kutta methods for Volterra integral equations to design a more stable and efficient algorithm. The constructed methods of orders \(1, 2\), and 3 are \(A_0\)-stable and the method of order 4 is \(A_0(\alpha)\)-stable. The capability of the proposed methods in solving stiff and nonstiff problems is shown by some numerical experiments.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
45D05 Volterra integral equations
65R20 Numerical methods for integral equations

Software:

DIMSIM
PDFBibTeX XMLCite
Full Text: DOI

References:

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