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The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type. (English) Zbl 0732.65122
The Ritz-Volterra projection for the initial-boundary-value problem for the parabolic Volterra integro-differential equation \(u_ t+A(t)u+\int^{t}_{0}B(t,\tau)u(\tau)d\tau =f\) was analyzed in detail by the first author, V. Thomeé and L. Wahlbin [SIAM J. Numer. Anal. 28, 1047-1070 (1991; Zbl 0728.65117)]. The present paper is concerned with the stability of this method and the derivation of \(L^{\infty}\) error estimates for certain special choices of the operators A(t) and B(t,\(\tau\)).

MSC:
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
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References:
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