2024 : 11 : 22

Mohammad Mehdizadeh

Academic rank: Professor
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Education: PhD.
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Faculty: 1
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Research

Title
A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs
Type
JournalPaper
Keywords
Explicit methods P-stable methods Singularly P-stable methods Obrechkoff methods Phase-fitted methods Symmetric multistep methods
Year
2020
Journal APPLIED MATHEMATICS AND COMPUTATION
DOI
Researchers Ali Shokri Shokri ، Mohammad Mehdizadeh

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.