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An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems. (English) Zbl 0983.65081
Summary: An efficient algorithm for the numerical integration of large sparse systems of stiff initial value ordinary differential equations and differential-algebraic equations is described. The algorithm is constructed by embedding a standard sparse linear algebraic equation solver into a suitably modified MEBDF code. An important practical application of this algorithm is in the numerical solution of time dependent partial differential equations, particularly in two or more space dimensions, using the method of lines. A code based on this algorithm is illustrated by application to several problems of practical interest and its performance is compared to that of the standard code LSODES.

MSC:
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L80 Numerical methods for differential-algebraic equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65Y15 Packaged methods for numerical algorithms
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