Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 923693, 9 pages
http://dx.doi.org/10.1155/2014/923693
Research Article

A Numerical Method for 1-D Parabolic Equation with Nonlocal Boundary Conditions

1Department of Mechanical Engineering, University of Colorado at Denver, Campus Box 112, P.O. Box 173364, Denver, CO 80217-3364, USA
2Department of Electrical Engineering, University of Colorado at Denver, Campus Box 112, P.O. Box 173364, Denver, CO 80217-3364, USA

Received 11 July 2014; Revised 2 November 2014; Accepted 3 November 2014; Published 20 November 2014

Academic Editor: Chengpeng Bi

Copyright © 2014 M. Tadi and Miloje Radenkovic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with a local method for the solution of one-dimensional parabolic equation with nonlocal boundary conditions. The method uses a coordinate transformation. After the coordinate transformation, it is then possible to obtain exact solutions for the resulting equations in terms of the local variables. These exact solutions are in terms of constants of integration that are unknown. By imposing the given boundary conditions and smoothness requirements for the solution, it is possible to furnish a set of linearly independent conditions that can be used to solve for the constants of integration. A number of examples are used to study the applicability of the method. In particular, three nonlinear problems are used to show the novelty of the method.