Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

A New Two-step Hybrid Singularly P-stable Method for the Numerical Solution of Second-order IVPs with Oscillating Solutions

Document Type : Research Paper

Authors
Ali Shokri 1
Mohammad Mehdizadeh Khalsaraei 2
Ali Atashyar 3
1 Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
2 Department of mathematics, University of Maragheh, Amirkabir Highway, P. O. Box. 55181-83111
3 Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
10.22052/ijmc.2020.224324.1493
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 Dufng's equation) as well as quantum chemistry problems (i.e. orbit problems of Stiefel and Bettis) indicated that the new method is superior, efcient, accurate and stable.
Keywords
Multiderivative methods
Oscillatory problems
Singularly P-stable methods
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Iranian Journal of Mathematical Chemistry
Volume 11, Issue 2
Summer 2020
Pages 113-132