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Izzo, G.; Russo, E.; Chiapparelli, C.

Highly stable Runge-Kutta methods for Volterra integral equations. (English) Zbl 1243.65157

Appl. Numer. Math. 62, No. 8, 1002-1013 (2012).
Summary: We investigate the numerical stability of the class of Runge-Kutta methods for the solution of Volterra integral equations of the second kind. To this aim we introduce the definition of \(V_{0}(\alpha )\)-stability and a new technique to construct highly stable methods. \(V_{0}\)-stable methods of order three and four are provided.

Cited in 9 Documents

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations

Keywords:

Runge-Kutta methods; nonlinear Volterra integral equations; linear stability analysis; convolution test equation; \(V_{0}\)-stability; \(V_{0}(\alpha )\)-stability; numerical examples

Software:

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References:

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