P-stable Hybrid Super-implicit Methods for Periodic Initial Value Problems


Authors

M. Mehdizadeh Khalsaraei - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran. M. Molayi - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran.


Abstract

This paper deals with a class of symmetric (hybrid) P-stable methods for the numerical solution of special second order initial value problems (IVPs). For linear multistep methods, Lambert and Watson [5], had shown that a P-stable method is necessarily implicit and that the maximum order attainable by a P -stable method is at most two. P-stability is important in the case of ’periodic stiffness’ as it is termed by Lambert and Watson [5], that is, when the solution consists of an oscillation of moderate frequency with a high frequency oscillation of small amplitude superimposed. In order to overcome the order-barrier on linear multistep P-stable methods, we developed a new type of implicit formulas of linear multistep methods. The formulas, which we call to be hybrid super-implicit, are of more implicitness than the socalled implicit formulas in the sense that they require the knowledge of functions not only at the past and present time-step but also at the future ones. In the cases when the right hand side of IVP is very complex, the super-implicit methods are preferred. Also, we have used off-step points which allow us to derive Pstable schemes of high order. We report numerical experiments to illustrate the accuracy and implementation aspects of this class of methods.


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ISRP Style

M. Mehdizadeh Khalsaraei, M. Molayi, P-stable Hybrid Super-implicit Methods for Periodic Initial Value Problems, Journal of Mathematics and Computer Science, 15 (2015), no. 2, 129-136

AMA Style

Khalsaraei M. Mehdizadeh, Molayi M., P-stable Hybrid Super-implicit Methods for Periodic Initial Value Problems. J Math Comput SCI-JM. (2015); 15(2):129-136

Chicago/Turabian Style

Khalsaraei, M. Mehdizadeh, Molayi, M.. "P-stable Hybrid Super-implicit Methods for Periodic Initial Value Problems." Journal of Mathematics and Computer Science, 15, no. 2 (2015): 129-136


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