Fourth-Order Approximation of the Fundamental Matrix of Linear System of Differential Equations

Abstract

A fourth-order approximation to the fundamental matrix of a system of linear differential equations is presented in closed form as a matrix exponential. The matrix exponential is then discretized over the interval of integration l‘adc approximation together with the method of scaling and squaning (Moler et at 1978) is used to evaluate the matrix exponential. This approach is suitable for solving both initial and boundary value problems with mixed boundary conditions. The approximating matrix can also be used as an integrating operator for methods which require information about the solution along the discretized subintervals. An example of a boundary value problem with mixed boundary condition is presented.