The implementation comparison between the Euler and trivial coupling schemes for achieving strong convergence

Yousef Alnafisah; Yousef Alnafisah

doi:10.3934/math.20231520

AIMS Mathematics

2023, Volume 8, Issue 12: 29701-29712. doi: 10.3934/math.20231520

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Research article

The implementation comparison between the Euler and trivial coupling schemes for achieving strong convergence

Yousef Alnafisah ^,

Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 23 July 2023 Revised: 02 October 2023 Accepted: 23 October 2023 Published: 02 November 2023
MSC : 34C10, 34K11

This study aimed to develop efficient numerical techniques with the same accuracy level as exact solutions of stochastic differential equations (SDEs). The MATLAB program was used to find solutions for the Euler and trivial coupling methods. The results of these methods were then compared and analyzed. The results show that Euler and trivial coupling methods give the same strong convergence. Furthermore, we demonstrated that these methods achieve strong convergence with a standard order of one-half to the exact solution of the SDE. Moreover, the Euler method is characterized by its speed, ease of application and ability to find solutions through computer programs.
- stochastic differential equations (SDEs),
- differential equations,
- trivial coupling method,
- Euler method,
- numerical solutions
Citation: Yousef Alnafisah. The implementation comparison between the Euler and trivial coupling schemes for achieving strong convergence[J]. AIMS Mathematics, 2023, 8(12): 29701-29712. doi: 10.3934/math.20231520

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Abstract

This study aimed to develop efficient numerical techniques with the same accuracy level as exact solutions of stochastic differential equations (SDEs). The MATLAB program was used to find solutions for the Euler and trivial coupling methods. The results of these methods were then compared and analyzed. The results show that Euler and trivial coupling methods give the same strong convergence. Furthermore, we demonstrated that these methods achieve strong convergence with a standard order of one-half to the exact solution of the SDE. Moreover, the Euler method is characterized by its speed, ease of application and ability to find solutions through computer programs.

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