Series Solutions of Multi-Layer Boundary Value Problems

It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value problems and seek approximate solutions. Many methods exist in the literature to numerically solve nonlinear boundary value problems. However, only few papers dealt with nonlinear multi- layer boundary value problems. In this work, we employ the homotopic analysis method (HAM) as the method of choice. We consider a real physical system dealing with the fluid flow in multi-channel porous media whose governing equations is exactly a nonlinear multi-layer boundary value problem.