This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the oper...This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B.展开更多
In this paper, the convergence analysis of the Volterra integral equation of second kind with weakly singular kernel and pantograph delays is provided. We use some function transformations and variable transformations...In this paper, the convergence analysis of the Volterra integral equation of second kind with weakly singular kernel and pantograph delays is provided. We use some function transformations and variable transformations to change the equation into a new Volterra integral equation with pantograph delays defined on the interval [-1, 1], so that the Jacobi orthogonal polynomial theory can be applied conveniently. We provide a rigorous error analysis for the proposed method in the L∞-norm and the weighted L2-norm. Numerical examples are presented to complement the theoretical convergence results.展开更多
文摘This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11271157, 11071102, 11001259）, the Croucher Foundation of Hong Kong, the National Center for Mathematics and Interdisciplinary Science, CAS, and the President Foundation of AMSS-CAS.
文摘In this paper, the convergence analysis of the Volterra integral equation of second kind with weakly singular kernel and pantograph delays is provided. We use some function transformations and variable transformations to change the equation into a new Volterra integral equation with pantograph delays defined on the interval [-1, 1], so that the Jacobi orthogonal polynomial theory can be applied conveniently. We provide a rigorous error analysis for the proposed method in the L∞-norm and the weighted L2-norm. Numerical examples are presented to complement the theoretical convergence results.
