Abstract
In this paper the Galerkin method is analyzed for the following nonlinear integro-differential equation of parabolic type:
Optimal L 2 error estimates for Crank-Nicolson and extrapolated Crank-Nicolson approximations are derived by using a non-classicalH 1 projection associated with the above equation. Both schemes result in procedures which are second order correct in time, but the latter requires the solution of a linear algebraic system only once per time step.
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Cannon, J.R., Lin, Y. Non-classicalH 1 projection and Galerkin methods for non-linear parabolic integro-differential equations. Calcolo 25, 187–201 (1988). https://doi.org/10.1007/BF02575943
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DOI: https://doi.org/10.1007/BF02575943