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Non-classical $$H^ 1$$ projection and Galerkin methods for non-linear parabolic integro-differential equations. (English) Zbl 0685.65124
The initial-boundary value problem for the equation $c(u)u_ t=\nabla \cdot \{a(u)\nabla u+\int^{t}_{0}b(x,t,r,u(x,r))\nabla u(x,r)dr\}+f(u\quad)$ is treated by Crank-Nicolson and extrapolated Crank-Nicolson approximations by using a non-classical $$H^ 1$$ projection method. Optimal $$L^ 2$$ error estimates are derived, and the schemes are shown to have second order accuracy in time. An advantage of the second scheme is that at each time-step only a linear algebraic system of equations is to be solved.
Reviewer: R.Gorenflo

##### MSC:
 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations
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##### References:
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