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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Block implicit one-step methods

Author: Daniel S. Watanabe
Journal: Math. Comp. 32 (1978), 405-414
MSC: Primary 65L05
MathSciNet review: 0494959
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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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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