Abstract
In this paper, the system of ordinary differential equations arisen from discretizing the convection–diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered. This system involves in computing e k A y for some vector y, where k is the time step-size and A is a large tridiagonal Toeplitz matrix. The common ways to compute an approximate solution of the convection–diffusion equation are based on replacing e k A y by an its approximation. We give an explicit expression for the exact value of e k A y and then the numerical results of our method with that of some well-known methods are compared.
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