Bernstein series solution of linear second‐order partial differential equations with mixed conditions | Zendy

Isik Osman Rasit | Zendy; Sezer Mehmet | Zendy; Guney Zekeriya | Zendy

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Bernstein series solution of linear second‐order partial differential equations with mixed conditions

Author(s) -

Isik Osman Rasit,

Sezer Mehmet,

Guney Zekeriya

Publication year - 2013

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.2817

Subject(s) - mathematics , residual , a priori and a posteriori , truncation error , series (stratigraphy) , numerical analysis , partial differential equation , norm (philosophy) , limit (mathematics) , mathematical analysis , algorithm , paleontology , philosophy , epistemology , political science , law , biology

The purpose of this study is to present a new collocation method for numerical solution of linear PDEs under the most general conditions. The method is given with a priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n , which gives better result in any norm ∥ ∥ . Finally, the effectiveness of the method is illustrated in some numerical experiments. Numerical results are consistent with the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

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