Numerical solution of space problems of potential theory. (Russian) Zbl 0674.65100
Variational-difference methods in problems of numerical analysis, Collect. Sci. Artic., 28-44 (1987).
[For the entire collection see Zbl 0673.00020.]
An integral equation of the first kind with a weak singularity in the kernel \[ (1)\quad \int_{\Gamma}u(x)R^{-1}(x,y)d\Gamma_ x=f(y) \] is considered. The goal of the paper is an investigation of conditions of existence, uniqueness and convergence of approximate solutions of equation (1) obtained by the Galerkin method and the collocation method in case of an approximation of the unknown density function by systems of piecewise constant functions.
An integral equation of the first kind with a weak singularity in the kernel \[ (1)\quad \int_{\Gamma}u(x)R^{-1}(x,y)d\Gamma_ x=f(y) \] is considered. The goal of the paper is an investigation of conditions of existence, uniqueness and convergence of approximate solutions of equation (1) obtained by the Galerkin method and the collocation method in case of an approximation of the unknown density function by systems of piecewise constant functions.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
