空间四阶-时间分数阶扩散波方程的一个新的数值分析方法

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空间四阶-时间分数阶扩散波方程的一个新的数值分析方法胡秀玲¹, 张鲁明²1. 江苏师范大学数学与统计学院, 徐州 221116;
2. 南京航空航天大学理学院, 南京 210016 A New Numerical Method for Fourth-order Fractional Diffusion-wave System HU Xiuling¹, ZHANG Luming²1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China;
2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

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摘要本文利用降阶法研究了空间四阶-时间分数阶扩散波方程的一个新的差分格式，用能量分析法证明了格式的无穷模稳定性和收敛性，并证明了格式的收敛阶为O，（τ^3-α+h²）.最后，数值实验验证了格式的精确度和有效性.

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收稿日期: 2012-05-08

PACS:

O241.82

基金资助:国家自然科学基金（11501262）资助项目.

引用本文:

胡秀玲, 张鲁明. 空间四阶-时间分数阶扩散波方程的一个新的数值分析方法[J]. 应用数学学报, 2017, 40(4): 543-561. HU Xiuling, ZHANG Luming. A New Numerical Method for Fourth-order Fractional Diffusion-wave System. Acta Mathematicae Applicatae Sinica, 2017, 40(4): 543-561.

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