Numerical Solution of Ninth and Tenth Order Ordinary Differential Equations via Hermite Wavelet Method

Abstract

In this paper, we study Hermite wavelet method (HWM) for numerical solutions of higher-order ordinary differential equations. The Hermite wavelet used Hermite polynomial which is the basis for this method. This technique uses collocation points that transform the differential equation into an algebraic system of equations which reduces difficult computations to easier form as compared with other numerical techniques. We consider and evaluate two test problems, one of them is of order nine and the other is of order ten in order to show the applicability of the method. The outcomes that we get from the considered approach are approximately similar to the exact solution and easily acquired. The absolute errors for different number of collocation points are calculated and compared with the results obtained by other methods present in the available literature, and the graphical results obtained showed comparison between present numerical results and analytical solutions. The proposed methodology is also computationally efficient relative to other numerical approaches and the results obtained via the proposed scheme are precise and correct.