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 two-step hybrid singularly P-stable method for the numerical solution of second-order IVPs with oscillating solutions
Type
JournalPaper
Keywords
Multiderivative methods; Oscillatory problems; Singularly P-stable methods
Year
2020
Journal Iranian Journal of Mathematical Chemistry
DOI
Researchers Ali Shokri Shokri ، Mohammad Mehdizadeh ، Ali Atashyar

Abstract

In this paper, a new two-step hybrid method of twelfth algebraic order is constructed and analyzed for the numerical solution of initial value problems of second-order ordinary differential equations. The proposed methods are symmetric and belongs to the family of multiderivative methods. Each methods of the new family appears to be hybrid, but after implementing the hybrid terms, it will continue as a multiderivative method. Therefore, the name semi-hybrid is used. The consistency, convergence, stability and periodicity of the methods are investigated and analyzed. The numerical results for some chemical (e.g. undamped Duffing's equation) as well as quantum chemistry problems (i.e. orbit problems of Stiefel and Bettis) indicated that the new method is superior, efficient, accurate and stable.