• Title/Summary/Keyword: difference norm bounds

Search Result 3, Processing Time 0.018 seconds

NEW BOUNDS FOR A PERTURBED GENERALIZED TAYLOR'S FORMULA

  • Cerone, P.;Dragomir, S.S.
    • East Asian mathematical journal
    • /
    • v.17 no.2
    • /
    • pp.197-215
    • /
    • 2001
  • A generalised Taylor series with integral remainder involving a convex combination of the end points of the interval under consideration is investigated. Perturbed generalised Taylor series are bounded in terms of Lebesgue p-norms on $[a,b]^2$ for $f_{\Delta}:[a,b]^2{\rightarrow}\mathbb{R}$ with $f_{\Delta}(t,s)=f(t)-f(s)$.

  • PDF

HYBRID DIFFERENCE SCHEMES FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS

  • Priyadharshini, R.Mythili;Ramanujam, N.;Tamilselvan, A.
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.5_6
    • /
    • pp.1001-1015
    • /
    • 2009
  • In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.

  • PDF

HYBRID DIFFERENCE SCHEMES FOR SINGULARLY PERTURBED PROBLEM OF MIXED TYPE WITH DISCONTINUOUS SOURCE TERM

  • Priyadharshini, R. Mythili;Ramanujam, N.;Valanarasu, T.
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.5_6
    • /
    • pp.1035-1054
    • /
    • 2010
  • We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.