Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model

IF 0.7 Q2 MATHEMATICS
Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei
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引用次数: 0

Abstract

The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.
求解分数阶种群扩散模型的自适应分层配置方法
分级种群扩散模型对害虫防治具有重要意义。本文提出了一种自适应分层配置方法来求解该模型,提高了基于组合恒等理论的低复杂度香农余弦小波算法的效率。这个函数是对以前构造的改进,减少了对参数迭代计算的需要,并具有插值、对称和紧凑支持等优点。该方法也可以推广到其他时间分数阶偏微分方程。算法的复杂度分析表明,在求解时间分数阶偏微分方程时,简洁函数比原始表达式具有效率优势。与Shannon-Gabor小波等其他小波谱方法相比,该方法具有更好的数值性能。
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