生物和化学过程中的时间分数反应-扩散合方程的动力学
Abdul Ghafoor1, Muhammad Fiaz2, Manzoor Hussain3
1Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, 26000, KP, Pakistan. abdulghafoor@kust.edu.pk.
Scientific reports
|March 30, 2024
概括
这项研究为时间分数反应-扩散模型提供了一个稳定的数值方法. 有限差异方法将复杂的分数模型简化为可解决的线性系统,在化学和生物模拟中被证明是有效的.
科学领域:
- 数字分析 数字分析
- 计算数学是指计算数学.
- 数学建模的数学建模
背景情况:
- 反应-扩散模型对于理解化学和生物过程至关重要.
- 与传统的整数顺序导数相比,时间分数导数提供了更准确的复杂现象表示.
- 对于非线性分数模型,现有的数值方法可能会面临稳定性和效率方面的挑战.
研究的目的:
- 开发和验证一个强大的数值策略来解决时间分数反应-扩散模型.
- 使用统一的方法来解决这些模型的线性和非线性情况.
- 确保拟议的数值方案准确,稳定和高效.
主要方法:
- 有限差的配方被用来分辨时间分数导数在卡普托的意义上.
- 一个方程公式近似卡普托导数,其次是剩余项的隐式方法.
- 准线性化用于处理非线性反应项,将其转化为线性代数系统.
- ·诺伊曼法用于严格评估数值方案的稳定性.
主要成果:
- 拟议的数值策略有效地将线性时间分数反应扩散模型减少到线性同时方程.
- 对于非线性模型,准线性化将分数系统转换为易于解决的线性代数系统.
- 使用·诺伊曼方法的稳定性分析证实,该数值方案是无条件稳定的.
- 该方法的适用性和准确性通过成功模拟各种基准模型,包括施纳肯伯格,格雷-斯科特和布鲁塞拉托模型来证明.
结论:
- 提出的基于有限差异的数值策略为时间分数反应-扩散模型提供了一种高效且无条件稳定的解决方案.
- 准线性化的集成有效地解决了非线性分数系统的复杂性.
- 经过验证的准确性和稳定性使该方法适用于化学和生物科学中的各种应用.
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