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Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis
Author(s) -
Barikbin Z.,
Keshavarz Hedayati E.
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22136
Subject(s) - mathematics , galerkin method , bernoulli differential equation , bernoulli polynomials , partial differential equation , bernoulli's principle , boundary value problem , basis (linear algebra) , mathematical analysis , algebraic equation , product (mathematics) , ritz method , basis function , partial derivative , differential equation , classical orthogonal polynomials , orthogonal polynomials , first order partial differential equation , exact differential equation , finite element method , geometry , physics , engineering , thermodynamics , aerospace engineering , nonlinear system , quantum mechanics
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