Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions

Autor: Bashar Zogheib, Emran Tohidi, Stanford Shateyi
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: Advances in Mathematical Physics, Vol 2017 (2017)
Druh dokumentu: article
ISSN: 1687-9120
1687-9139
DOI: 10.1155/2017/5691452
Popis: 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.
Databáze: Directory of Open Access Journals
Externí odkaz: