Original A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions

The focus of this paper is to develop and improve a higher-order Haar wavelet approach for solving nonlinear singularly perturbed differential equations with various pairs of boundary conditions like initial, boundary, two points, integral and multi -point integral boundary conditions. The theoretical convergence and computational stability of the method is also presented. The comparison of the proposed higher-order Haar wavelet method is performed with the recent published work including the well-known Haar wavelet method in terms of convergence and accuracy. In the nonlinear case, a quasilinearization technique has been adopted. The proposed method is easy to implement on various boundary conditions, and the computed results are high-order accurate, stable and efficient. We have also checked the satisfactory performance of the proposed method for nonlinear differential equations having no analytical solution in some of the test problems. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.