A Text Book on Solution of Partial Differential Equations using OCFE

This is basically a review of the technique of orthogonal collocation on finite elements (OCFE) method which is used to solve not only linear differential equations but is quite useful for the solution of non linear equations as well. First of all an introduction of orthogonal polynomials like Jacobi, Legendre and Chebyshev polynomial is presented. Then orthogonal collocation method is discussed for symmetric and non symmetric problems. Technique to form discretization matrices, selection of collocation points and quadrature weights is presented. The method of orthogonal collocation on finite elements is discussed in details about its application to various problems. Basically, OCFE is a combination of two methods finite element method (FEM) and orthogonal collocation method (OCM). OCM discretizes Boundary Value Problems conveniently where as FEM provides accuracy to the solution.