跨境电商快速发展背景下一类线性经济发展系统解的方法研究
Research on the Method of Solving a Class of Linear Economic Development Systems in the Context of Rapid Cross-Border E-Commerce Development
摘要: 经济增长问题在宏观经济理论研究中占有重要地位，是国家经济繁荣昌盛的一个前提。经济增长能推动跨境电商的发展且有效激发市场主体，跨境电商的发展同样为经济的增长做出了很大贡献，由此产生了各种经济增长模型和理论。在当今跨境电商快速发展的背景下，研究线性经济发展系统的解的方法尤为重要。故研究了混合Filon渐近方法，该方法旨在解决一类经济系统模型的求解问题。最后通过实验验证了该方法的有效性，为经济决策提供了有效的帮助。
Abstract: The issue of economic growth holds a significant position in macroeconomic theory research and serves as a prerequisite for a country’s economic prosperity. Economic growth not only propels the development of cross-border e-commerce but also effectively stimulates market entities. Conversely, the development of cross-border e-commerce has made substantial contributions to eco-nomic growth. This interplay has led to the emergence of various economic growth models and theories. In the context of the rapid development of cross-border e-commerce today, it is particularly important to study the solutions for linear economic development systems. Therefore, the hybrid Filon asymptotic method has been researched, which addresses the issue of how to solve a class of economic system models. Finally, experimental results have verified the effectiveness of this method, providing valuable assistance for economic decision-making.
文章引用：班良雪. 跨境电商快速发展背景下一类线性经济发展系统解的方法研究[J]. 电子商务评论, 2024, 13(4): 5282-5291. https://doi.org/10.12677/ecl.2024.1341763

参考文献

[1] 赵慧, 葛春瑞, 马婷. 电子商务环境与经济增长——基于设立跨境电商综合试验区的准自然实验[J]. 甘肃行政学院学报, 2021(5): 114-124+128.
[2] 赵亚南, 张瑞, 赵宏伟. 跨境电商对地区经济的影响文献综述[J]. 现代营销(下旬刊), 2024(8): 96-98.
[3] 兰天. 全球经济下行对我国跨境电商的影响[J]. 现代营销(经营版), 2020(8): 124-125.
[4] 张红梅, 刘会茹, 蔡惠萍, 等. 线性经济发展系统解的性质研究[J]. 数学的实践与认识, 2010, 40(23): 226-233.
[5] Filon, L.N.G. (1930) On a Quadrature Formula for Trigonometric Integrals. Proceedings of the Royal Society of Edinburgh, 49, 38-47. [Google Scholar] [CrossRef] 
[6] Iserles, A. and Nørsett, S.P. (2004) On Quadrature Methods for Highly Oscillatory Integrals and Their Implementation. BIT Numerical Mathematics, 44, 755-772.
[7] Iserles, A. and Nørsett, S.P. (2005) Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461, 1383-1399.
[8] 赵龙斌. 高振荡积分及积分方程的数值方法研究[D]: [博士学位论文]. 武汉: 华中科技大学, 2017.
[9] Wang, H. and Xiang, S. (2010) Asymptotic Expansion and Filon-Type Methods for a Volterra Integral Equation with a Highly Oscillatory Kernel. IMA Journal of Numerical Analysis, 31, 469-490. [Google Scholar] [CrossRef] 
[10] Ma, J., Xiang, S. and Kang, H. (2013) On the Convergence Rates of Filon Methods for the Solution of a Volterra Integral Equation with a Highly Oscillatory Bessel Kernel. Applied Mathematics Letters, 26, 699-705. [Google Scholar] [CrossRef] 
[11] Xiang, S. and Brunner, H. (2013) Efficient Methods for Volterra Integral Equations with Highly Oscillatory Bessel Kernels. BIT Numerical Mathematics, 53, 241-263. [Google Scholar] [CrossRef] 
[12] Xiang, S. and Wu, Q. (2013) Numerical Solutions to Volterra Integral Equations of the Second Kind with Oscillatory Trigonometric Kernels. Applied Mathematics and Computation, 223, 34-44. [Google Scholar] [CrossRef] 
[13] Fang, C., Ma, J. and Xiang, M. (2015) On Filon Methods for a Class of Volterra Integral Equations with Highly Oscillatory Bessel Kernels. Applied Mathematics and Computation, 268, 783-792. [Google Scholar] [CrossRef] 
[14] Brunner, H. (2014) On Volterra Integral Operators with Highly Oscillatory Kernels. Discrete & Continuous Dynamical Systems A, 34, 915-929. [Google Scholar] [CrossRef] 
[15] Ma, J. (2017) Oscillation-free Solutions to Volterra Integral and Integro-Differential Equations with Periodic Force Terms. Applied Mathematics and Computation, 294, 294-298. [Google Scholar] [CrossRef] 
[16] Brunner, H., Ma, Y. and Xu, Y. (2015) The Oscillation of Solutions of Volterra Integral and Integro-Differential Equations with Highly Oscillatory Kernels. Journal of Integral Equations and Applications, 27, 455-487. [Google Scholar] [CrossRef] 
[17] Fang, C., He, G. and Xiang, S. (2019) Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels. Symmetry, 11, 232-248. [Google Scholar] [CrossRef] 
[18] Zhao, L. and Wang, P. (2022) Error Estimates of Piecewise Hermite Collocation Method for Highly Oscillatory Volterra Integral Equation with Bessel Kernel. Mathematics and Computers in Simulation, 196, 137-150. [Google Scholar] [CrossRef] 
[19] Zhao, L. and Huang, C. (2022) The Generalized Quadrature Method for a Class of Highly Oscillatory Volterra Integral Equations. Numerical Algorithms, 92, 1503-1516. [Google Scholar] [CrossRef] 
[20] 方春华, 李明亮, 田维. Hermite配置法求解第一类Volterra积分方程[J]. 湖南理工学院学报(自然科学版), 2018, 31(4): 7-10.
[21] Wang, J., Fang, C. and Zhang, G. (2023) Effective Collocation Methods to Solve Volterra Integral Equations with Weakly Singular Highly Oscillatory Fourier or Airy Kernels. International Journal of Computer Mathematics, 100, 1532-1551. [Google Scholar] [CrossRef] 
[22] Wang, J., Fang, C., Zhang, G. and Zhang, Z. (2023) Modified Collocation Methods for Second Kind of Volterra Integral Equations with Weakly Singular Highly Oscillatory Bessel Kernels. Journal of Applied Analysis & Computation, 13, 3231-3252. [Google Scholar] [CrossRef] 

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