Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method

Abstract

A numerical procedure is developed to obtain the solution of a mathematical model for capillary formation in tumor angiogenesis. The proposed method is based on the shifted Legendre tau technique. Our approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution as a shifted Legendre polynomial with unknown coefficients. The operational matrices of integral and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative example is included to demonstrate the validity and applicability of the presented technique.