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

An efficient algorithm for the numerical integration of large sparse systems of stiff initial value ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) 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 (PDEs), particularly in two or more space dimensions, using the method of lines (MOL). 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.