Approximation of the Modied Error Function by Using Perturbative and Sinc Collocation Methods

Supriya Mandal; Debabrata Singh; M. M. Panja

Supriya Mandal Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.
Debabrata Singh Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.
M. M. Panja Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.

Keywords: Modified error function, Error function, Nonlinear ordinary differential equation, Perturbative approximation of modified error function, Sinc function, Truncated cardinal function representation

Abstract

This chapter deals with the evaluation of some integrals involving error-, exponential- and algebraic functions with an objective to present explicit expressions for the second and third order correction terms in the approximation of the modified error function in the perturbation approach. Over and above an approximation of the desired modified error function has been developed in sinc basis. The accuracy in the approximation (perturbation method and sinc basis) have been compared with the approximate value available in the literature. Results obtained by perturbation approximation and scheme based on sinc basis seem to be useful in the study of Stefan problem. The results obtained here appear to be new and resolve the lack of desired monotonicity property in the results derived earlier e.g. by Ceretania et al.[1].