Bernstein Ritz‐Galerkin method for solving an initial‐boundary value problem that combines Neumann and integral condition for the wave equation |
| |
Authors: | SA Yousefi Z Barikbin Mehdi Dehghan |
| |
Institution: | 1. Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran;2. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran |
| |
Abstract: | In this article, the Ritz‐Galerkin method in Bernstein polynomial basis is implemented to give an approximate solution of a hyperbolic partial differential equation with an integral condition. We will deal here with a type of nonlocal boundary value problem, that is, the solution of a hyperbolic partial differential equation with a nonlocal boundary specification. The nonlocal conditions arise mainly when the data on the boundary cannot be measured directly. The properties of Bernstein polynomial and Ritz‐Galerkin method are first presented, then Ritz‐Galerkin method is used to reduce the given hyperbolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique presented in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 |
| |
Keywords: | Bernstein basis Boundary value problem Nonlocal boundary condition Ritz‐Galerkin method Second‐order hyperbolic equation Wave equation |
|
|