A numerical algorithm based on modified orthogonal linear spline for solving a coupled nonlinear inverse reaction--diffusion problem

Abstract

In this paper, a modified orthogonal linear spline (OL--spline) is used for the numerical solution of a coupled nonlinear inverse reaction–diffusion problem to determine the unknown boundary conditions. The convergence properties of the new linear combination are obtained. A quasi--linearization technique is utilized to linearize the nonlinear term in the equations. This process, produces a linear system of equations which can be solved easily. Using the new inequalities, error estimation and convergence of the proposed method are investigated. Two numerical examples are given to demonstrate the computational efficiency of the method and also the experimental convergence rate of examples are obtained.