Integration operators for first order linear matrix differential equations

Abstract

The choice of an optimum approximate integration operator for systems of first order linear differential equations is discussed, with emphasis on the achievable accuracy. The approximations include the whole family of one-step direct schemes and a new modally uncoupled operator, both using a piecewise lincar representation of the forcing function. It is concluded that the modal operator has many advantages if one pays the price for the preliminary eigenvalue problem. Among direct schemes the trapezoidal scheme is found to be superior except in matters of short-time accuracy for problems with fast-varying boundary conditions.