Abstract
Waveform relaxation (WR) methods for second order equations y′’=f(t,y), y(t 0)=y 0, y′(t 0)=y′ 0 are studied. For linear case, the method converges superlinearly for any splittings of the coefficient matrix. For nonlinear case, the method converges quadratically only for waveform Newton method. It is shown, however, that the method with approximate Jacobian matrix converges superlinearly. The accuracy, execution times and speedup ratios of the WR methods on a parallel computer are discussed.
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Ozawa, K., Yamada, S. (1998). Waveform relaxation for second order differential equation y′’=f(x,y) . In: Pritchard, D., Reeve, J. (eds) Euro-Par’98 Parallel Processing. Euro-Par 1998. Lecture Notes in Computer Science, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057930
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DOI: https://doi.org/10.1007/BFb0057930
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