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Stability and convergence of a class of continuous piecewise polynomial approximations for time-fractional differential equations
来源:LASG    访问次数:    报告时间:2018-8-28
【报告人】        周晗 博士
【报告人单位】河北工业大学理学院
【报告时间】    2018年8月28日(星期二)10:00
【报告地点】    新楼1118会议室
【报告简介】    Fractional calculus, as a generalization of ordinary calculus, has been an interesting topic since the 17th century. Recently, there are some attractive applications in the fields of physics, chemistry and engineering by applying fractional integrals and derivatives to construct mathematical models that describes anomalous diffusion process. In this report, we propose and study a class of numerical schemes to approximate time-fractional differential equations. The methods are based on the approximations to the Caputo fractional derivative of order from 0 to 1, which are strongly related to the backward differentiation formulae. We investigate their theoretical properties, such as the truncation errors with respect to sufficiently smooth solutions, and the numerical stability. Numerical experiments are given to verify our theoretical investigations.
 
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