We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form y D Ay C g.t/ and y D Ay C g.t/, where y.t/ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term g.t/, constructed with the help of the truncated singular value decomposition. The second stage is a special residual-based block Krylov subspace method. The accuracy of the method is… CONTINUE READING