Solving delay differential equations by Runge-Kutta method using different types of interpolation
Introduction to delay differential equations (DDEs) and the areas where they arise are given. Analysis of specific numerical methods for solving delay differential equation is considered. A brief discussion on Runge-Kutta method when adapted to delay differential equation is introduced. Embedded...
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| 格式: | Thesis |
| 語言: | English English |
| 出版: |
2001
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| 主題: | |
| 在線閱讀: | http://psasir.upm.edu.my/id/eprint/9237/1/FSAS_2001_17.pdf |
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| 總結: | Introduction to delay differential equations (DDEs) and the areas where they
arise are given. Analysis of specific numerical methods for solving delay differential
equation is considered. A brief discussion on Runge-Kutta method when adapted to
delay differential equation is introduced.
Embedded Singly Diagonally Implicit Runge-Kutta (SDIRK) method of
third order four-stage in fourth order five-stage which is more attractive from the
practical point of view is used to solve delay differential equations. The delay term is
approximated using three types of interpolation that is the divided difference
interpolation, Hermite interpolation and In't Hout interpolation. Numerical results
based on these three interpolations are tabulated and compared.
Finally, the stability properties of SDIRK method when applied to DDEs
using Lagrange interpolation and In't Hout interpolation are investigated and their
regions of stability are presented. |
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