Legendre wavelet-based iterative schemes for fourth-order elliptic equations with nonlocal boundary conditions

Abstract

In the literature of wavelets, there is limited report of work done to solve nonlinear differential equations with nonlocal boundary conditions. This work is a new attempt to solve a fourth-order elliptic equation with the use of nonlocal boundary conditions by coupling quasilinearization with Legendre wavelet. Since the previously available approach failed to produce reliable accuracy for certain class of problems, this iterative scheme has been suitably modified to deal with a broader class to obtain an accuracy that is reliable. To show the efficiency of the proposed numerical method, a comparison was performed with some existing methods available in the literature. © 2019, Springer-Verlag London Ltd., part of Springer Nature.