Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

HIGHER ORDER OF FULLY DISCREATE SOLUTION FOR PARABOLIC PROBLEM IN $L_{\infty}$

  • Lee, H.Y. (Department of Mathematics Kyungsung University) ;
  • Lee, J.R. (Department of Mathematics Kyungsung University)
  • Published : 1997.03.01

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Abstract

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

Keywords

References

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