1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution...1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution (v) does not depend continuously on the data (g). In order to treat the ill-posedness and develop the numerical method, one reformulates the problem as a Volterra integral equation of the first kind wish a convolution type kernel (see Sneddon [1], Carslaw and Jaeger [2])展开更多
In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for...In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.展开更多
文摘1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution (v) does not depend continuously on the data (g). In order to treat the ill-posedness and develop the numerical method, one reformulates the problem as a Volterra integral equation of the first kind wish a convolution type kernel (see Sneddon [1], Carslaw and Jaeger [2])
文摘In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.
