自共轭椭圆型偏微分方程奇异摄动问题的一致收敛差分解法
A Uniformly Convergent Difference Scheme for the Singular Perturbation of a Self-adjoint Elliptic Partial Differential Equation
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摘要: 本文在矩形域内考虑高阶导数项含有小参数的自共轭椭圆型第一边值问题. 本文,我们应用渐近分析方法建立了一种新的差分格式,比较了差分方程的解与微分方程的解的渐近性态,并证明了解的一致收敛性.Abstract: In this paper,we consider a self-adjoint elliptic first boundary value problem with a small parameter affecting the highest derivative.In the paper,we set up a new scheme by the asymptotic analysis method,compare asymptotic behavior between the solution of the difference equation and the solution of the differential equation,and show uniform convergence of the new scheme.
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[1] Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Method for Problems with Initial and Boundary Laye.(1980). [2] 苏煜城、吴启光,椭圆一抛物偏微分方程奇异摄动问题的差分解法,应用数学和力学.1,2(1980). [3] 苏煜城.奇异摄动中的边界层校正法,上海科学技术出版社(1983).
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