Two-point Taylor polynomial iterative linearization <i>via</i> Legendre nodes for exothermic diffusion model

Abstract

A novel approach was devised to solve an exothermic diffusion model by employing an iterative linearization method that utilizes a two-point Taylor polynomial and Legendre roots. The procedure commences with the process of linearization and thereafter addresses the nonlinear problem by employing the Legendre root collocation technique. Iterative solutions are derived by the repeated application of Legendre root collocation method until the intended solutions are attained. The accuracy of the procedure was assessed through the utilization of measures such as comparison with referenced results and the calculation of relative absolute error.