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