An O(h6) numerical solution of general nonlinear fifth-order two point boundary value problems

Abstract  A sixth-order numerical scheme is developed for general nonlinear fifth-order two point boundary-value problems. The standard
sextic spline for the solution of fifth order two point boundary-value problems gives only O(h
²) accuracy and leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations
of the problem are generated and applied to construct the numerical algorithm. O(h
⁶) global error estimates obtained for these problems. The convergence properties of the method is studied. This scheme has
been applied to the system of nonlinear fifth order two-point boundary value problem too. Numerical results are given to illustrate
the efficiency of the proposed method computationally. Results from the numerical experiments, verify the theoretical behavior
of the orders of convergence.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-010-9362-4
• Authors
  
  
  • Jalil Rashidinia, Iran University of Science & Technology Narmak School of Mathematics Tehran 16844-13114 Iran
  • M. Ghasemi, Iran University of Science & Technology Narmak School of Mathematics Tehran 16844-13114 Iran
  • R. Jalilian, Ilam University Department of Mathematics P.O. Box 69315-516 Ilam Iran
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

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Original source : http://www.springerlink.com/content/4303h2p61403nr...