Block implicit one-step methods-Reference-Cited by-同舟云学术

Block implicit one-step methods

Published:1978 Issue:142 Volume:32 Page:405-414
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Watanabe Daniel S.

Abstract

A new class of block implicit one-step methods for ordinary differential equations is presented. The methods are based on quadrature and generate function values at nonmesh points through Hermite interpolation. A general convergence theorem for block implicit methods is given, and the stability of the new class of methods is analyzed. The class contains A-stable, stiffly stable, strongly A-stable, and strongly stiffly stable methods. Numerical results demonstrating the efficiency and effectiveness of a particular block method are presented.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1978-32-142/S0025-5718-1978-0494959-0/S0025-5718-1978-0494959-0.pdf

Reference14 articles.

1. Natural spline block implicit methods;Andria, George D.;Nordisk Tidskr. Informationsbehandling (BIT),1973

2. D. BARTON, I. M. WILLERS & R. V. M. ZAHAR, "Taylor series methods for ordinary differential equations—an evaluation," in Mathematical Software (J. R. Rice, Editor), Academic Press, New York, 1971, pp. 369-390.

3. A new method of solving nonlinear simultaneous equations;Broyden, C. G.;Comput. J.,1969

4. Implicit Runge-Kutta processes;Butcher, J. C.;Math. Comp.,1964

5. F. H. CHIPMAN, Numerical Solution of Initial Value Problems Using A-Stable Runge-Kutta Processes, Ph. D. Thesis, Univ. of Waterloo, Waterloo, Ontario, 1971.

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