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 Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation

主讲人：赵景军

摘要：This report is mainly concerned with the construction and convergence of Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation. Under some conditions, we first prove the existence and uniqueness of its exact solution. Then, we present the collocation methods for this problem. The main idea is to discretize the distributed-order fractional differential equation into a multi-term fractional differential equation by the Gauss-Legendre quadrature formula, and to approximate the multi-term one by the Legendre-Gauss collocation method. Moreover, we provide the convergence estimate for the proposed methods in the weighted $L^{2}$-norm.

主讲人简介：赵景军，哈尔滨工业大学数学学院教授、博士生导师。哈尔滨工程大学兼职教授、博士生导师。曾访问剑桥大学、阿尔伯塔大学、香港大学、中科院数学与系统科学研究院。现任黑龙江省工业与应用数学学会常务理事。主要从事微分方程数值解的研究。在SIAM J. Numer. Anal.和J. Sci. Comput.等期刊发表SCI论文80余篇，主持和参加国家自然科学基金、国防预研基金多项。先后获中国高校自然科学二等奖、黑龙江省科学技术二等奖。

邀请人：李东方

时间：2025年4月23日10:00-13:00

地点：腾讯会议室：870569131