三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析

THE A.D.I. GALERKIN METHODS AND THE ANALYSIS FOR 3-DIMENSIONAL NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION

研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计.

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.