Fast Collocation Methods for High-Dimensional Weakly Singular Integral Equations
نویسندگان
چکیده
منابع مشابه
Fully Discrete Collocation Method for Weakly Singular Integral Equations
Abstract. To find the approximate solutions of a weakly singular integral equation by the collocation method it is necessary to solve linear systems whose coefficients are expressed as integrals. These integrals cannot usually be computed exactly. We get the fully discrete collocation method when we approximate the integrals by quadrature formulas on nonuniform grid. In this paper an appropriat...
متن کاملCOLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS
In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of Fredholm-Volterra integral equations (FVIEs) are smooth.
متن کاملApproximate Solution of Weakly Singular Integral Equations by Iterative Methods
In present paper we elaborated the numerical schemes of iterative methods for an approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Ti...
متن کاملcollocation method for fredholm-volterra integral equations with weakly kernels
in this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of fredholm-volterra integral equations (fvies) are smooth.
متن کاملA Nodal Spline Collocation Method for Weakly Singular Volterra Integral Equations
A collocation method based on optimal nodal splines is presented for the numerical solution of linear Volterra integral equations of the second kind with weakly singular kernel. Since the considered spline operator is a bounded projector we can prove that, for sequences of locally uniform meshes, the approximate solution error converges to zero at exactly the same optimal rate as the spline app...
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 Integral Equations and Applications
سال: 2008
ISSN: 0897-3962
DOI: 10.1216/jie-2008-20-1-49