Slodička, Marián Numerical solution of a parabolic equation with a weakly singular positive-type memory term. (English) Zbl 0898.65102 Electron. J. Differ. Equ. 1997, Paper 9, 12 p. (1997). The author considers a numerical solution of an initial and boundary value problem for a parabolic integro-differential equation whose integral is the convolution product of a positive definite weakly singular kernel with the time derivative of the solution. The author describes a product integration method for the discretization of the Volterra term in the equation. The equation is discretized in space by linear finite elements, and in time by the backward-Euler method. The author proves existence and uniqueness of a solution to the continuous problem, demonstrates that some regularity is present, and establishes convergence of the approximation scheme to a solution that satisfies mile regularity. Reviewer: M.Z.Nashed (Newark/Delaware) Cited in 9 Documents MSC: 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:parabolic integro-differential equation; weakly singular kernel; convolution; product integration method; finite elements; backward-Euler method; convergence PDFBibTeX XMLCite \textit{M. Slodička}, Electron. J. Differ. Equ. 1997, Paper 9, 12 p. (1997; Zbl 0898.65102) Full Text: EMIS