Product integration methods for second-kind Abel integral equations
نویسندگان
چکیده
منابع مشابه
Galerkin Methods for Second Kind Integral Equations
This paper discusses the numerical solution of Fredholm integral equations of the second kind which have weakly singular kernels and inhomogeneous terms. Global convergence estimates are derived for the Galerkin and iterated Galerkin methods using splines on arbitrary quasiuniform meshes as approximating subspaces. It is observed that, due to the singularities present in the solution being appr...
متن کاملConvergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
Abstract This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel φ(t, s) = (t − s)−μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233: 938– 950], the error analysis for this approach is carried out for 0 < μ < 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a ...
متن کاملFractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
Fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular Volterra integral equations. The proposed methods are convergent of the order of the underlying multistep method, also in the generic case of solutions which are not smooth at the origin. The stability properties (stability region, A-stability, A(a)-stability) are closely related to those o...
متن کاملProduct integration for Volterra integral equations of the second kind with weakly singular kernels
We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.
متن کاملWavelet Galerkin methods for second-kind integral equations
We use vector-valued multiwavelets on compact sets to develop a Galerkin method for systems of integral equations of the second kind. We propose a compression strategy for the coeflieient matrix of the linear system obtained from this method and show that the compressed scheme preserves almost optimal convergence rate of the original scheme and yields a sparse matrix with a bounded condition nu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1984
ISSN: 0377-0427
DOI: 10.1016/0377-0427(84)90027-x