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Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions
Joint Authors
Zogheib, Bashar
Shateyi, Stanford
Tohidi, Emran
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-22
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions.
The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients.
By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES.
Operational matrices of differentiation are implemented for speeding up the operations.
In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation.
Several numerical examples are provided to show the efficiency and spectral (exponential) accuracy of the proposed method.
American Psychological Association (APA)
Zogheib, Bashar& Tohidi, Emran& Shateyi, Stanford. 2017. Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123226
Modern Language Association (MLA)
Zogheib, Bashar…[et al.]. Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions. Advances in Mathematical Physics No. 2017 (2017), pp.1-15.
https://search.emarefa.net/detail/BIM-1123226
American Medical Association (AMA)
Zogheib, Bashar& Tohidi, Emran& Shateyi, Stanford. Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123226
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123226