Title：Numerical methods for fractional differential equations with initial or boundary singularities
Speaker：Cao,Wanrong（曹婉容）
Affiliation：Southeast University
Time：14:30 - 15:30, September 28th (Tuesday), 2021
Venue: Academic Hall, 1st Floor, Nanjing Center for Applied Mathematics 4 Liye Zone, TusCity, 26 Zhishi Rd, Chi-Lin Innovation Park, Nanjing
Inviter：刘继军教授
Abstract：We present efficient numerical schemes for solving fractional initial value problems and fractional boundary value problems with non-smooth solution. Firstly, based on the known structure of solution, correction terms are introduced to construct an IMEX scheme for nonlinear fractional initial value problems, which is of uniform second-order convergence and has good stability than explicit schemes. Secondly, for fractional boundary value problems, an extrapolation technique is exploited to improve the existing finite difference schemes, which can avoid low accuracy of numerical solutions caused by low regularity of the exact solution. The algorithm can be used to solve high dimensional problems. Numerical examples verify the theoretical findings and show the efficiency of the presented numerical schemes.
报告人介绍：曹婉容，教授，博士生导师。东南大学数学学院副院长，中国系统仿真学会仿真算法专业委员会委员，江苏省工业与应用数学学会秘书长。主讲《金融模型及计算》、《数值代数》、工科研究生《数值分析》等课程，主编教学参考书《数值分析全真试题解析》。长期从事微分方程数值方法的研究，在国内外计算数学核心期刊上发表学术论文三十余篇。目前的研究兴趣为随机微分方程、分数阶微分方程及延迟微分方程的高效数值方法，包括数值方法的建立、收敛性与稳定性分析、刚性及非线性问题的数值算法，以及生物、控制、金融等领域中相关应用问题的数值模拟与大规模计算等。主持完成国家自然科学基金项目2项，主持在研国家自然科学基金项目1项。