The operational matrix of Legendre polynomials for solving nonlinear thin film flow problems

Abstract

In this paper, the operational matrix with Legendre polynomials method will be implemented to get the approximate solution for the nonlinear thin film flow (NTFF) of third grade problem. This method provides an approximate solution by converting the nonlinear differential equation into nonlinear algebraic equations system which can be solved by using Mathematica® 10. To illustrate the accuracy and efficiency of the proposed method, the maximum error remainder was calculated. The results obtained from using the proposed method have proven to be accurate, reliable and effective. In addition, the approximate solution is compared with the fourth order Runge-Kutta method (RK4) and good agreement has been achieved.

Keywords

• Nonlinear differential equations
• Approximate solution
• Legendre polynomials
• The thin film flow
• Operational matrix