Ritz‐Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non‐classic boundary conditions

Abstract

Purpose

The purpose of this paper is to implement the Ritz‐Galerkin method in Bernstein polynomial basis to give approximation solution of a parabolic partial differential equation with non‐local boundary conditions.

Design/methodology/approach

The properties of Bernstein polynomial and Ritz‐Galerkin method are first presented, then the Ritz‐Galerkin method is utilized to reduce the given parabolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Findings

The authors applied the method presented in this paper and solved three test problems.

Originality/value

This is the first time that the Ritz‐Galerkin method in Bernstein polynomial basis is employed to solve the model investigated in the current paper.

Citation

Yousefi, S.A., Barikbin, Z. and Dehghan, M. (2012), "Ritz‐Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non‐classic boundary conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 1, pp. 39-48. https://doi.org/10.1108/09615531211188784