Journal Article

The Differential Variant and Its Error Estimate for the Class of Non-Overdetermined Third Order Ordinary Differential Equation

Abstract

The tau method for the numerical solution of Ordinary Differential Equations (ODEs) seeks an approximant of the solution which exactly satisfies the corresponding Perturbed Ordinary Differential Equations (PODE). This tau approximant has the power of x as its basis function. In this paper, the differential variant of the tau method for initial value problems(IVPs) in the class of nonoverdetermined third order ordinary differential equations is considered. The corresponding error estimate for the variant is obtained and numerical results for some selected problems were provided. The order of the approximant is closely captured based on the numerical evidences obtained.

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