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Extrapolation of Explicit DIMSIMs of High Order to Solve the Ordinary Differential Equations
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作者 Ali J. Kadhim annie gorgey 《Journal of Applied Mathematics and Physics》 2019年第12期3022-3030,共9页
The purpose of this research is to investigate the effciency of explicit diagonally implicit multi-stage integration methods with extrapolation. The author gave detailed explanation of explicit diagonally implicit mul... The purpose of this research is to investigate the effciency of explicit diagonally implicit multi-stage integration methods with extrapolation. The author gave detailed explanation of explicit diagonally implicit multi-stage integration method and compared the base method with a technique known as extrapolation to improve the effciency. Extrapolation for symmetric Runge-Kutta method is proven to improve the accuracy since with extrapolation the solutions exhibit asymptotic error expansion, however for General linear methods, it is not known whether extrapolation can improve the effciency or not. Therefore this research focuses on the numerical experimental results of the explicit diagonally implicit multistage integration with and without extrapolation for solving some ordinary differential equations. The numerical results showed that the base method with extrapolation is more effcient than the method without extrapolation. 展开更多
关键词 EXTRAPOLATION Technique General Linear METHODS Diagonally Implicit Muti-Stage Integration EXPLICIT METHODS
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Extrapolation of GLMs with IRKS Property to Solve the Ordinary Differential Equations
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作者 Ali J. Kadhim annie gorgey 《American Journal of Computational Mathematics》 2019年第4期251-260,共10页
The extrapolation technique has been proved to be very powerful in improving the performance of the approximate methods by large time whether engineering or scientific problems that are handled on computers. In this p... The extrapolation technique has been proved to be very powerful in improving the performance of the approximate methods by large time whether engineering or scientific problems that are handled on computers. In this paper, we investigate the efficiency of extrapolation of explicit general linear methods with Inherent Runge-Kutta stability in solving the non-stiff problems. The numerical experiments are shown for Van der Pol and Brusselator test problems to determine the efficiency of the explicit general linear methods with extrapolation technique. The numerical results showed that method with extrapolation is efficient than method without extrapolation. 展开更多
关键词 EXTRAPOLATION Technique General Linear METHODS Inherent RUNGE-KUTTA Stability EXPLICIT METHODS
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