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

Isik O. R., Sezer M., Guney Z.

Mathematical Methods in the Applied Sciences, vol.37, no.5, pp.609-619, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.1002/mma.2817
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.609-619
  • Keywords: residual error estimation, Bernstein series solution, collocation method, numerical solution of PDEs
  • Manisa Celal Bayar University Affiliated: Yes

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.