【作者】 刘建军；

【导师】 曹学年；

【作者基本信息】 湘潭大学 ， 计算数学， 2007， 硕士

【摘要】 近年来，分数阶微分方程问题在现代科学技术领域获得了日益广泛的应用。由于其勿庸置疑的重要性，国内外对于分数阶微分方程问题数值方法的研究正在蓬勃兴起。因此，开展分数阶微分方程数值方法的研究具有重要理论意义和实用价值。本文分为四个部分。在第二章中给出了求解分数阶微分方程问题的三类数值方法，即分数阶欧拉方法，分数阶BDF方法以及分数阶降阶BDF方法。第三章进行了方法的稳定性分析，获得了方法的稳定域。第四章给出了方法的相容阶。第五章对文中所提出的数值方法进行了数值试验，特别就计算生物学中的两个分数阶微分方程问题进行测试，数值结果表明方法是有效的。文中最后一部分对论文所做的主要工作进行了总结并对今后的工作提出展望。更多还原

【Abstract】 In recent years, the extensive application of the fractional differential equation in many modern scientific technique realms makes the research of its numerical method in and abroad prospers. Therefore, the research of numerical method of the fractional differential equation is of important theory significance and practical value.This thesis consists of five chapters. Chapter 2 introduces the linear multi-step method of the fractional differential equation which includes Fractional Order Euler method, Fractional Order BDF method, and Fractional Order decline order BDF method. Chapter 3 A stability analysis that carried on the method, acquired stable area of the method, Chapter 4 give method of consist order. Chapter 5 to text the numerical method put forward carries on the numerical experiment, special two fractional differential equation problem within biologies carries on the test, the number result enunciation method is valid. The article last part we carry on summary’s combine to this text to put forward the outlook to the work of the future.更多还原