New wavelet method for solving ordinary differential equations

In this paper a new wavelet formula is derived based on the definition of the convolution between the Haar and CAS wavelets, with finding the integrals of the suggested formula analytically. The outlines of the suggested method with the collocation points are written for solving ordinary differential equations of second-order. From the comparison of the numerical results of the proposed methods with the exact solution to solve three problems, we concluded that the suggested method is more accurate, better, and nearer to the exact solution.