Hermite wavelet method for approximate solution of higher order boundary value problems of ordinary differential equations

In this paper, Hermite wavelet method (HWM) is considered for numerical solution of 12- and 13-order boundary value problems (BVPs) of ordinary differential equations (ODEs). The proposed algorithm for HWM developed in Maple software converts the ODEs into an algebraic systems of equations. These algebraic equations are then solved by evaluating the unknown constants present in the system of equations and the approximate solution of the problem is obtained. Test problems are considered and their solutions are investigated using HWM-based algorithm. The obtained results from the test problems are compared with exact solution, and with other numerical methods solution in the existing literature. Results comparison are presented both graphically and in tabular form showing close agreement with exact solution, and greater accuracy than homotopy perturbation method (HPM) and differential transform method (DTM).