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The Computer Journal 1968 11(3):305-310; doi:10.1093/comjnl/11.3.305
© 1968 by British Computer Society
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Stable high order implicit methods for the numerical solution of systems of differential equations

G. J. Makinson *

Department of Computational and Statistical Science, The University, P.O. Box 147, Liverpool, UK

Some stable high order implicit methods for the solution of a system of differential equations of the form

[equation: see PDF]

where M is a constant banded matrix or of special form, are given.

They require the solution at each step of more than one set of simultaneous linear equations but the coefficient matrix is the same for each set. Applications to the numerical solution of the heat conduction equation are given.

First received November 1967. revised form May 1968.

* Department of Computational and Statistical Science, The University, P.O. Box 147, Liverpool.


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