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The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem

Author

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  • Surla, K.
  • Uzelac, Z.
  • Teofanov, Lj.

Abstract

We consider a singularly perturbed boundary value problem with two small parameters. The problem is numerically treated by a quadratic spline collocation method. The suitable choice of collocation points provides the discrete minimum principle. Error bounds for the numerical approximations are established. Numerical results give justification of the parameter-uniform convergence of the numerical approximations.

Suggested Citation

  • Surla, K. & Uzelac, Z. & Teofanov, Lj., 2009. "The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2490-2505.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:8:p:2490-2505
    DOI: 10.1016/j.matcom.2009.01.007
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    Cited by:

    1. Ahsan, Muhammad & Bohner, Martin & Ullah, Aizaz & Khan, Amir Ali & Ahmad, Sheraz, 2023. "A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 166-180.
    2. Toprakseven, Şuayip & Zhu, Peng, 2023. "Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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