A-Stable and L-Stable Block Implicit One-Step Method

A-Stable and L-Stable Block Implicit One-Step Method

Year:    1985

Journal of Computational Mathematics, Vol. 3 (1985), Iss. 4 : pp. 328–341

Abstract

A class of methods for solving the initial problem for ordinary differential equations are studied. We develop k-block implicit one step methods whose nodes in a block are nonequidistant. When the components of the node vector are related to the zeros of Jacobi's orthogonal polynomials, we can derive a subclass of formulas which are A or L-stable. The order can be arbitrarily high with A- or L-stability. We suggest a modified algorithm which avoids the inversion of a $km×km$ matrix during Newton-Raphson iterations, where $m$ is the number of differential equations. When k=4, for example, only a couple of $m×m$ matrices have to be inversed, but four values can be obtained at one time.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1985-JCM-9629

Journal of Computational Mathematics, Vol. 3 (1985), Iss. 4 : pp. 328–341

Published online:    1985-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords: