Variable order step size method for solving orbital problems with periodic solutions
Existing variable order step size numerical techniques for solving a system of higher-order ordinary differential equations (ODEs) requires direct calculating the integration coefficients at each step change. In this study, a variable order step size is presented for direct solving higher-order or...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Published: |
Lviv Polytechnic National University
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102585/ https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-9-number-1-2022/variable-order-step-size-method-solving-orbital |
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| Summary: | Existing variable order step size numerical techniques for solving a system of higher-order ordinary differential equations (ODEs) requires direct calculating the integration
coefficients at each step change. In this study, a variable order step size is presented
for direct solving higher-order orbital equations. The proposed algorithm calculates the
integration coefficients only once at the beginning and, if necessary, once at the end. The
accuracy of the numerical approximation is validated with well-known orbital differential
equations. To reduce computational costs, we obtain the relationship for the predictor-corrector algorithm between integration coefficients of various orders. The efficiency of
the proposed method is substantiated by the graphical representation of accuracy at the
total evaluation steps. |
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