A Note on Numerical Transform Calculus

Many of the numerical transform methods, developed for the solution of integrodifferential equations, exhibit difficulties when discontinuities occur at the origin. In this paper a procedure for including initial conditions is derived which effectively takes origin discontinuities into account. Although shown to be applicable to a number of transform methods, the derivation emphasizes application to the z-form integration operators because of their relatively greater accuracy. Numerical examples illustrating the solution of a constant coefficient and a time-varying problem are given. The technique is equally applicable to the solution of nonlinear problems.