A high-order reliable and efficient Haar wavelet collocation method for nonlinear problems with two point-integral boundary conditions

The primary goal of this study is to increase and improve the precision and order of convergence of the well-known Haar wavelet collocation method (HWCM) that is named as Higher order Haar wavelet collocation method (HHWCM). The HHWCM will then be applied to nonlinear ordinary differential equations with a variety of initial conditions, boundary conditions, periodic conditions, two-point conditions, integral conditions, and multi-point integral boundary conditions. The paper also contains important theorem about the convergence of the HHWCM with computational stability. The convergence of HHWCM is then compared to recently published works including the famous HWCM. In nonlinear case the quasilinearization process has been introduced to linearize the differential equation. Different orders of differential equations including homogeneous and non–homogeneous equations with constant and variable coefficients are also tested by HHWCM. The key advantages of the HHWCM include its easy to use, stability, convergence, high order accuracy, and efficiency under a range of boundary conditions. We have also implemented the HHWCM on nonlinear differential equation having no exact solution.