ERROR ANALYSIS OF FRACTIONAL COLLOCATION METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH NONCOMPACT OPERATORS  

作　　者：Zheng Ma Chengming Huang Anatoly A.Alikhanov 

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China [3]North-Caucasus Center for Mathematical Research,North-Caucasus Federal University,Stavropol 355017,Russia [4]North-Eastern Federal University,Yakutsk 677000,Russia

出　　处：《Journal of Computational Mathematics》2025年第3期690-707,共18页计算数学(英文)

基　　金：supported by the National Natural Science Foundation of China(Grant No.12171177);supported by the Russian Science Foundation(Grant No.23-41-00037).

摘　　要：This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact operators.The focus is on the problems with weakly singular solutions.To handle the initial weak singularity of the solution,a fractional collocation method is applied.A rigorous hp-version error analysis of the numerical method under a weighted H1-norm is carried out.The result shows that the method can achieve high order convergence for such equations.Numerical experiments are also presented to confirm the effectiveness of the proposed method.

关 键 词：Volterra integro-differential equation Noncompact operator Nonsmooth solution Collocation method Fractional polynomial hp-version error analysis 

分 类 号：O241.8[理学—计算数学]