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Convergence results for continuous-time waveform methods for Volterra integral equations. (English) Zbl 0855.65142

The paper deals with iterative methods (the waveform relaxation (WR) methods) for solving systems of second kind Volterra integral equations. A different approach to the parallelism, the parallelism “across space”, is considered and continuous-time waveform relaxation methods are also investigated. Many particular methods (Picard method, Jacobi method, Gauss-Seidel method, Newton method, Richardson method) are discussed from the point of view of their convergence properties. Particular attention is devoted to parallel WR methods, since they are particularly suitable in solving large systems of Volterra integral equations.

MSC:

65R20 Numerical methods for integral equations
45G15 Systems of nonlinear integral equations
65Y05 Parallel numerical computation
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