Block implicit one-step methods

Author:
Daniel S. Watanabe

Journal:
Math. Comp. **32** (1978), 405-414

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1978-0494959-0

MathSciNet review:
0494959

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0494959-0

Keywords:
Ordinary differential equations,
methods based on quadrature,
Hermite interpolation,
*A*-stable,
stiffly stable,
strongly *A*-stable,
strongly stiffly stable

Article copyright:
© Copyright 1978
American Mathematical Society