A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs

Ali Shokri and Mohammad Mehdizadeh Khalsaraei

Applied Mathematics and Computation, 2020, vol. 376, issue C

Abstract: According to Lambert and Watson [6], Theorem 4 says that the linear multistep P-stable methods can not be explicit; they must be implicit and being implicit is the essential condition to obtain important feature of P-stability. Few explicit P-stable methods have been created in which they are nonlinear or at most P-stable. For the first time in literature, in this paper, we create a new family of explicit linear two-step singularly P-stable methods with phase-lag of order infinity for the numerical solution of initial value problems of second-order ordinary differential equations. Finally, the numerical results obtained by the new family for some well-known problems show its superiority in efficiency, accuracy, convergency and stability.

Keywords: Explicit methods; P-stable methods; Singularly P-stable methods; Obrechkoff methods; Phase-fitted methods; Symmetric multistep methods (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:376:y:2020:i:c:s0096300320300850

DOI: 10.1016/j.amc.2020.125116

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