An Inproved Algorithm for Matrix Functions Appeared in Exponential Integrators

Abstract

Abstract. The exponential integrator is one of the powerful methods for solving systems of ordinary differential equations. In this method, the computation of certain matrix functions, usually called φ functions, is an important issue. For the efficient computations of these functions, the scaling and squaring technique based on rational approximations is used. There exist two rational approximation methods. For each of the two methods the computational cost is evaluated and compared. For the best method, a modified squaring technique is applied to reduce roundoff errors. Numerical experiments show that the modified technique improves the accuracy by about 2 decimal digits.