On convergence of quadrature-differences method for linear singular integro-differential equations on the interval. (English) Zbl 1090.45003

Fedotov, A. I.

Arch. Math., Brno 37, No. 4, 257-271 (2001).

Summary: Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval \((-1, 1)\). We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.

MSC:

45E05	Integral equations with kernels of Cauchy type
45L05	Theoretical approximation of solutions to integral equations
65R20	Numerical methods for integral equations

Keywords:

singular integro-differential equations; quadrature-differences method