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<p>In this paper, we deal with the numerical positivity, boundedness and convergence for the Wright-Fisher model. For the efficient numerical approximation of the Wright-Fisher model, a linearly implicit Euler method with truncated Wiener process is introduced. In comparison to the balanced implicit method (BIM), balanced implicit split step (BISS) method, and semi-discrete (SD) scheme, its discrete form is simpler and can be simulated easily. We prove the convergence of the method, and numerical experiments show that the convergence order of the scheme is 1/2. Finally, we give numerical examples to illustrate the positivity, boundedness and convergence of the proposed scheme, and compare it with the SD, BIM and BISS schemes. The numerical results verify the theoretical findings.</p>

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Boundary preservation and convergence of the linearly implicit Euler method with truncated Wiener process for the Wright-Fisher model

  • 期刊论文

  • 发表日期：

    2025年5月10日

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  • Jianguo Tan,
  • Yaqi An

摘要

In this paper, we deal with the numerical positivity, boundedness and convergence for the Wright-Fisher model. For the efficient numerical approximation of the Wright-Fisher model, a linearly implicit Euler method with truncated Wiener process is introduced. In comparison to the balanced implicit method (BIM), balanced implicit split step (BISS) method, and semi-discrete (SD) scheme, its discrete form is simpler and can be simulated easily. We prove the convergence of the method, and numerical experiments show that the convergence order of the scheme is 1/2. Finally, we give numerical examples to illustrate the positivity, boundedness and convergence of the proposed scheme, and compare it with the SD, BIM and BISS schemes. The numerical results verify the theoretical findings.