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系统科学与数学 2001
THE A.D.I. GALERKIN METHODS AND THE ANALYSIS FOR 3-DIMENSIONAL NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION
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Abstract:
The A. D. I. Galerkin schemes for 3-dimensional nonlinear parabolic integro- differential equation are studied. By using alternating direction, the 3-dimensional problem is reduced to a family of single space Variable problems, the calculating work is simplified; by using Galerkin method, the high accuracy property is obtained. The influence coming from the Volterra term is treated successfully; the stability and convergence properties for both Galerkin and A.D.I. Galerkin schemes are demonstrated, the optical H1-norm and L2-norm estimates are obtained.