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

Authorsعباس سعادتمندی,مهدی دهقان
JournalCommunications in numerical methods in engineering
Page number1467
Volume number24
IFثبت نشده
Paper TypeFull Paper
Published At2008-11-01
Journal GradeScientific - research
Journal TypeElectronic
Journal CountryIran, Islamic Republic Of
Journal IndexSCOPUS ,JCR

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.

tags: numerical solution; shifted Legendre tau method; capillary formation; tumor angiogenesis; operational matrix