Numerical Solution of Singularly Perturbed Boundary Value Problems Based on Optimal Control Strategy

Abstract  In this paper, we develop a numerical technique for singularly perturbed boundary value problems using B-spline functions
and least square method. The approximate solution derived in this article is convergent to the exact solution and can be applied
both to linear and nonlinear models. The numerical examples and computational results illustrate and guarantee a higher accuracy
for this technique.

• Content Type Journal Article
• DOI 10.1007/s10440-009-9553-y
• Authors
  
  
  • G. B. Loghmani, University of Yazd Department of Mathematics Yazd Iran
  • M. Ahmadinia, University of Qom Department of Mathematics Qom Iran
  
  

• Journal Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications
• Online ISSN 1572-9036
• Print ISSN 0167-8019

Published by

Original source : http://www.springerlink.com/content/r53431354628m5...

A nonstandard mixed finite element family

Abstract  We show that standard mixed finite element methods, of second or higher degree, for second order elliptic equations can be
modified by imposing additional continuity conditions for the flux, which reduces the dimension of the space. This reduced
space still gives a stable method with an optimal order of convergence. We recall our postprocessing method and the a posteriori
error estimator based on this.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0272-0
• Authors
  
  
  • Rolf Stenberg, Helsinki University of Technology–TKK Institute of Mathematics and Systems Analysis P. O. Box 1100 02015 TKK Helsinki Finland
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

Published by

Original source : http://www.springerlink.com/content/b466866m423196...

Numerical simulation of the modified regularized long wave equation by He's variational iteration method

The modified regularized long wave (MRLW) equation, with some initial conditions, is solved numerically by variational iteration method. This method is useful for obtaining numerical solutions with high degree of accuracy. The variational iteration solution for the MRLW equation converges to its exact solution. Moreover, the conservation laws properties of the MRLW equation are also studied. Finally, interaction of two and three solitary waves is shown. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Published by

Original source : http://dx.doi.org/10.1002%2Fnum.20537...