Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis
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...
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| Published in | Numerical methods for partial differential equations Vol. 33; no. 4; pp. 1143 - 1158 |
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| Language | English |
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01.07.2017
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| Abstract | 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 |
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| AbstractList | 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 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. [copy 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143-1158, 2017 |
| Author | Barikbin, Z. Keshavarz Hedayati, E. |
| Author_xml | – sequence: 1 givenname: Z. surname: Barikbin fullname: Barikbin, Z. email: barikbin@ikiu.ac.ir organization: Imam Khomeini International University – sequence: 2 givenname: E. surname: Keshavarz Hedayati fullname: Keshavarz Hedayati, E. organization: Buein Zahra Technical University |
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| SubjectTerms | 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 |
| Title | Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis |
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