A GENERALIZED FORMULATION FOR INTEGRATED VARIANT OF TAU METHOD FOR OVERDETERMINED M-TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The tau method approximates the solution of a differential equation with a polynomial. This is the exact solution of a differential equation obtained by adding to the right hand side of the given equation a perturbation term, consisting of suitably chosen linear combination of polynomials. In this paper, a generalized formula or recurrence relation for the integrated variant of the tau method was derived which captures the general class of problems involving m-th order ordinary differential equations (ODEs) To validate this result, the generalized form was casted as a theorem for which mathematical induction principle was used to prove the result.