Hybrid methods for solving special fourth order ordinary differential equations
In recent time, Runge-Kutta methods that integrate special fourth or- der ordinary differential equations (ODEs) directly are proposed to ad- dress efficiency issues associated with classical Runge-Kutta methods. Although, the methods require approximation of y′, y′′ and y′′′ of the solution at...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80109/1/3.pdf http://psasir.upm.edu.my/id/eprint/80109/ https://einspem.upm.edu.my/journal/fullpaper/vol13sapril/3.pdf |
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| Summary: | In recent time, Runge-Kutta methods that integrate special fourth or-
der ordinary differential equations (ODEs) directly are proposed to ad-
dress efficiency issues associated with classical Runge-Kutta methods.
Although, the methods require approximation of y′, y′′ and y′′′ of the
solution at every step. In this paper, a hybrid type method is proposed,
which can directly integrate special fourth order ODEs. The method
does not require the approximation of any derivatives of the solution.
Algebraic order conditions of the methods are derived via Taylor series
technique. Using the order conditions, eight algebraic order method is
presented. Absolute stability of the method is analyzed and the stabil-
ity region presented. Numerical experiment is conducted on some test
problems. Results from the experiment show that the new method is
more efficient and accurate than the existing Runge-Kutta and hybrid
methods with similar number of function evaluation. |
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