Solution of homogeneous ordinary linear differential systems by numerical inversion of Laplace transforms

Algorithms based on the numerical inversion of Laplace transforms are developed for computing the solution x(¿) of a homogeneous ordinary linear differential system of the form dx/d¿ = Ax. The local truncation error and the stability of the algorithms are analysed. It is shown how the algorithms can be made unconditionally stable and how the local truncation error can be minimised.