An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions | Zendy

Emran Tohidi | Zendy; Adem Kılıçman | Zendy

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An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions

Author(s) -

Emran Tohidi,

Adem Kılıçman

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/369029

Subject(s) - mathematics , legendre polynomials , algebraic equation , collocation (remote sensing) , partial differential equation , sinc function , matrix (chemical analysis) , boundary value problem , collocation method , mathematical analysis , algebraic number , parabolic partial differential equation , differential equation , ordinary differential equation , computer science , nonlinear system , physics , materials science , quantum mechanics , machine learning , composite material

The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy

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