Enhanced resolution in solving first-order nonlinear differential equations with integral condition: a high-order wavelet approach

In this article, the Haar wavelet collocation method (HWCM) is proposed for the numerical solution of a first-order nonlinear differential equation with a two-point integral condition. A nonlinear ordinary differential equation with an initial condition, an integral condition, or a two-point integral condition can be solved using the proposed technique in a straightforward manner. Two nonlinear test problems have been solved: one with an integral condition and the other with a two-point integral condition. The accuracy of the proposed method is significantly higher than that of the traditional Haar wavelet technique.