Higher-Order Singular BVP Emerging in the Semiconductor Industry: Analysis and Computation of Solutions

Abstract

In this work, we consider a class of non-linear, singular, non-self-adjoint, fourth-order, and singular BVP arising in the semiconductor industry. We investigate the theoretical and numerical results of solutions for the governing model corresponding to different boundary conditions by considering the domain as a disk of any radius T > 0. Problems are difficult to analyze the solutions due to their characteristics. Moreover, it has no exact solutions. Additionally, there are two solutions to these problems. So, it becomes difficult to apply any discrete approach to obtain both approximate solutions. We develop an iterative method based on boundary conditions that gives numerical approximations. The convergence analysis of the technique is discussed. Some numerical examples are given to show the efficiency and accuracy of the method.