Numerical Solution of Non Linear Differential Equation by Using Shooting Techniques

Abstract

Many problems that occur in physics and engineering can be modelled by linear or nonlinear differential equations. In this paper we find the solution of Blasius type equations which are nonlinear ordinary differential equations on a semi-infinite interval. The Blasius equation is a third-order non-linear ordinary differential equation. The non-linear mathematical model of the problem prohibits the use of the analytical methods. A numerical solution is the single approach for these problems. The two-point boundary problem was solved by a Runge-Kutta method and shooting method. Matlab functions make numerical solution of the mathematical models of the fluid flow relatively simple and quick solutions are presented for Blasius equations with additional computations based on the numerical results obtained by the Matlab function. Numerical study on boundary layer equation due to stationary flat plate, Matlab is the mathematical programming that used to solve the boundary layer equation applied toolbox method. The numerical results show a good agreement with the exact solution of Blasius equation and consistent with prior published result. The accuracy of the proposed method is higher than other approximation analytical solutions; hence suggest that proposed method is efficient and practical.