عنوان مجله
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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL
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کلیدواژهها
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Numerical simulation, initial-value problems, hybrid, P-stable, Obrechkoff methods, second-order initial-value problems
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چکیده
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In this paper, a new family of two-step semi-hybrid schemes of the 12th algebraic order is proposed for the numerical
simulation of initial-value problems of second-order ordinary differential equations. The proposed methods are symmetric
and belong to the family of multiderivative methods. Each method of the new family appears to be hybrid, but
after implementing the hybrid terms, it will continue as a multiderivative method. Therefore, the designation semi-hybrid
is used. The consistency, convergence, stability, and periodicity of the methods are investigated and analyzed. In order to
show the accuracy, consistency, convergence, and stability of the proposed family, it was tested on some well-known
problems, such as the undamped Duffing’s equation. The simulation results demonstrate the efficiency and advantages of
the proposed method compared to the currently available methods.
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