Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

• Published in: Numerical methods for partial differential equations Vol. 33; no. 4; pp. 1143 - 1158
• Main Authors: Barikbin, Z., Keshavarz Hedayati, E.
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01.07.2017
• Subjects: Approximation; Bernoulli polynomials basis; Boundary conditions; boundary value problem; Differential equations; Exact solutions; Heat equations; integral boundary conditions; Mathematical analysis; Mathematical models; one‐dimensional parabolic equation; Polynomials; product solution; Ritz–Galerkin method
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.22136

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017