Haar Wavelet Method for the Solution of Fourteenth Order Boundary Value Problems

Abstract

Higher-order boundary value problems (BVP) of differential equations (DEs) are important in the mathematical description of many real-world processes. Solving such problems for exact or analytical solutions is not always easy to deal. Therefore, to compute their numerical solution, we need some numerical methods. Hence, in this work, a powerful numerical procedure based on Haar Wavelet (HW) method is established to deal with fourteenth-order BVPs linear and nonlinear. A generalized form of the algorithm is developed under general boundary conditions. Then the numerical method is verified on various examples from the literature. Also, maximum and root mean square errors are calculated. Moreover, a comparison between exact and numerical results is shown at different collocation points. Furthermore, convergence rate is approximately 2 at various numbers of nodal points is also calculated.