Bernstein series solution of linear second‐order partial differential equations with mixed conditions |
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| Authors: | Osman Rasit Isik Mehmet Sezer Zekeriya Guney |
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| Affiliation: | 1. Elementary Mathematics Education Program, Faculty of Education, Mugla Sitki Kocman University, , Mugla 48000, Turkey;2. Department of Mathematics, Faculty of Sciences and Arts, Manisa Celal Bayar University, , 45000 Manisa, Turkey;3. Department of Mathematics, Faculty of Education, Mugla Sitki Kocman University, , 48000 Mugla, Turkey |
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| Abstract: | 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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| Keywords: | numerical solution of PDEs collocation method Bernstein series solution residual error estimation |
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