An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems.

*(English)*Zbl 0983.65081Summary: 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 |

##### Keywords:

stiff systems; Burgers equation; packaged method; algorithm; large sparse systems; differential-algebraic equations; MEBDF; method of lines; performance
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\textit{T. J. Abdulla} et al., Comput. Math. Appl. 42, No. 1--2, 121--129 (2001; Zbl 0983.65081)

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