EFFICIENT COMPUTATION OF THE MATRIX EXPONENTIAL USING PADE-APPROXIMATION

A modified Pade approximation has been proposed to calculate the matrix exponential involved in the numerical solution of linear evolution equations. If the exponential matrix has a band structure, a factorization method may then be conveniently used to reduce computation flops. Numerical solutions of the heat-conduction equation and time-dependent Schrodinger equation are given as numerical examples to illustrate the feasibility. An increase in efficiency and accuracy over conventional methods is obtained.