2-stage explicit total variation diminishing preserving Runge-Kutta methods

Document Type : Research Paper

Authors

University of Maragheh

Abstract

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities.

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References

[1] R. Anguelov, Total variation diminishing nonstandard finite difference schemes for conservation laws, J. Math. Comput 51 (2010), 160-166.
[2] M. Mehdizadeh Khalsaraei, An improvement on the positivity results for 2-stage explicit Runge-Kutta methods, J. Comput. Appl. Math 235 (2010), 137-143.
[3] B. Koren, A robust upwind discretization for advection, diffusion and source terms. In: Numerical Methods for Advection-Diffusion Problems, Notes on Numerical Fluid Mechanics 45 (1993), 117-138.
[4] C.W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput 9 (1988), 1073-1084.
[5] A. Harten, High resolution schemes for hyperbolic conservation laws, SJournal of Computational Physics 49 (1983), 357-393.
[6] W. Hundsdorfer, J. G. Verwer Numerical Solution of Time-Dependent Advection Diffusion-Reaction Equation, Springer (2003)

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History

  • Receive Date: 14 December 2013
  • Accept Date: 14 December 2013

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