The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass

Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial...

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Published inJournal of computational and applied mathematics Vol. 235; no. 17; pp. 5272 - 5283
Main Authors Yousefi, S.A., Behroozifar, M., Dehghan, Mehdi
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.07.2011
Elsevier
Subjects
Approximation
Bernstein basis
Boundaries
Exact sciences and technology
Integral condition
Mathematical analysis
Mathematical models
Mathematics
Matrices
Matrix methods
Nonlocal boundary conditions
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
One-dimensional parabolic equation
Operational matrices
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Specification of mass
Specifications
Integral condition
Nonlocal boundary conditions
Bernstein basis
One-dimensional parabolic equation
Operational matrices
Specification of mass
Integration
Initial value problem
Polynomial equation
Numerical method
Boundary condition
Stochastic method
Partial differential equation
Implementation
Bernstein polynomial
Parabolic equation
Numerical analysis
Boundary value problem
One-dimensional calculations
Applied mathematics
Algebraic equation
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Abstract Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions. The properties of Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of 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. ► A discrete complex-valued bidirectional associative memory network is considered. ► Sufficient condition is given for stored patterns to be fixed points of the network. ► Each fixed point is shown to belong to a fixed point group of four fixed points.
AbstractList Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions. The properties of Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of 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. ► A discrete complex-valued bidirectional associative memory network is considered. ► Sufficient condition is given for stored patterns to be fixed points of the network. ► Each fixed point is shown to belong to a fixed point group of four fixed points.
Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions. The properties of Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of 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.
Author Yousefi, S.A.
Dehghan, Mehdi
Behroozifar, M.
Author_xml – sequence: 1
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  surname: Yousefi
  fullname: Yousefi, S.A.
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  organization: Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran
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  givenname: M.
  surname: Behroozifar
  fullname: Behroozifar, M.
  email: m_behroozifar@nit.ac.ir
  organization: Faculty of Basic Sciences, Babol University of Technology, Babol, Mazandaran, Iran
– sequence: 3
  givenname: Mehdi
  surname: Dehghan
  fullname: Dehghan, Mehdi
  email: mdehghan@aut.ac.ir, mdehghan.aut@gmail.com
  organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran, Iran
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Issue 17
Keywords Integral condition
Nonlocal boundary conditions
Bernstein basis
One-dimensional parabolic equation
Operational matrices
Specification of mass
Integration
Initial value problem
Polynomial equation
Numerical method
Boundary condition
Stochastic method
Partial differential equation
Implementation
Bernstein polynomial
Parabolic equation
Numerical analysis
Boundary value problem
One-dimensional calculations
Applied mathematics
Algebraic equation
Language English
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Snippet Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this...
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SubjectTerms Approximation
Bernstein basis
Boundaries
Exact sciences and technology
Integral condition
Mathematical analysis
Mathematical models
Mathematics
Matrices
Matrix methods
Nonlocal boundary conditions
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
One-dimensional parabolic equation
Operational matrices
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Specification of mass
Specifications
Title The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass
URI https://dx.doi.org/10.1016/j.cam.2011.05.038
https://www.proquest.com/docview/1671283502
Volume 235
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