A Singularly Perturbed Reaction-Diffusion Problem with Incompatible Boundary-Initial Data

  • J. L. Gracia
  • E. O’Riordan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


A singularly perturbed reaction-diffusion parabolic problem with an incompatibility between the initial and boundary conditions is examined. A finite difference scheme is considered which utilizes a special finite difference operator and a piecewise uniform Shishkin mesh. Numerical results are presented for both nodal and global pointwise convergence, using bilinear interpolation and, also, an interpolation method based on the error function. These results show that the method is not globally convergent when bilinear interpolation is used but they indicate that, for the test problem considered, it is globally convergent using the second type of interpolation.


Test Problem Global Convergence Parabolic Problem Bilinear Interpolation Singularly Perturb 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • J. L. Gracia
    • 1
    • 2
  • E. O’Riordan
    • 1
    • 2
  1. 1.IUMA. Department of Applied MathematicsUniversity of ZaragozaSpain
  2. 2.School of Mathematical SciencesDublin City UniversityIreland

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