An optimized explicit TDRK method for solving oscillatory problems


Authors

Yong Wang - School of Business, Linyi University, Linyi, Shandong, 276005, P. R. China. Min Sun - School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China. Hongchun Sun - School of Business, Linyi University, Linyi, Shandong, 276005, P. R. China.


Abstract

In this paper, a new optimized explicit two-derivative Runge-Kutta (TDRK) method with frequencydepending coeficients is proposed, which is derived by nullifying the dispersion, the dissipation, and the first derivative of the dispersion. The new method has algebraic order four and is dispersive of order five and dissipative of order four. In addition, the phase analysis of the new method is also presented. Numerical experiments are reported to show the efficiency of the new method.


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