Generic algorithms for solving ODE using the Tau method with an error estimation

The Tau method is an accurate and efficient method for the numerical solution of ordinary differential equation (O.D.E) with polynomial coefficients. In [1] Adeniyi et al., we derived a recursive formula for a fast reliable computational error estimate of Tau method. In the present work, we present the generic algorithms for solving O.D.E. using the Tau method. The pseudocodes describing the algorithms are in C-like language. The algorithms are assembled into a reusable Tau objects' Class Hierarchy (TOCH) with specification given in the interface definition language (IDL) representation and implemented using the C+ + Programming language.