Software for Initial Value Problems

All of the following codes are written in Fortran and each implements Modified Extended Backward Differentiation Formulae (MEBDF). The MEBDF are described, for example, in the book by Hairer and Wanner [6].

MEBDFDAE

The MEBDFDAE code is designed to solve stiff Initial Value Problems for systems of ordinary differential equations (ODEs)

Y´ = F(T,Y),

and linearly implicit differential algebraic equations (DAEs)

M Y´ = F(T,Y)

where M is a constant matrix.

• Source code

• Numerical tests



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MEBDFV

The MEBDFV code is designed to solve stiff Initial Value Problems for systems of linearly implicit differential algebraic equations

M(Y) Y´ = F(T,Y).

This code is an extension of the code MEBDFDAE since it allows the mass matrix M to depend on Y.

• Source code

• Numerical tests



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MEBDFI

The MEBDFI code is designed to solve Initial Value Problems for systems of implicit differential algebraic equations of the general form

G(T,Y,Y´)=0.

• Source code

• Numerical tests



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MEBDFSO

The MEBDFSO code is designed to solve stiff Initial Value Problems for very large sparse systems of ODEs of the form

Y´ = F(T,Y).

In this code the linear equation solver is replaced by the sparse solver YSMP [3]. This code is of particular use in the solution of time dependent partial differential equations using the method of lines.

• Source code

• Sparse linear algebra solver (YALE)

• Numerical tests



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MEBDFSD

The MEBDFSD code is designed to solve stiff Initial Value Problems for very large sparse systems of DAEs of the form

M Y´ = F(T,Y),

where M is a constant matrix. In this code the sparse solver used is MA28 [2]. Again this code has applications in the method of lines solution of time dependent PDEs.

• Source code

• Sparse linear algebra solver (MA28)

• Numerical tests



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