双曲-抛物偏微分方程奇异摄动问题的差分解法
A Difference Method for Singular Perturbation Problem of Hyperbolic-Parabolic Partial Differential Equation
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摘要: 本文对双曲-抛物偏微分方程奇异摄动问题构造了一个指数型拟合差分格式.我们不仅在方程中加了一个拟合因子,而且在逼近第二个初始条件时也加了拟合因子.我们利用问题的渐近解证明了差分格式关于小参数的一致收敛性.Abstract: In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation. Not only do we take a fitting factor in the equation, but also we put one in the approximation of second initial condition. By means of the asymptotic solution of singular perturbation problem we proved the uniform convergence of this scheme with respect to the small parameter.
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[1] Вишик М.И.и Л.А.Люстерник,Регулярное вырождение и пограничный слойдля линейных дифференциалъных уравнений с малым парамером,УМН,12,5(77) [2] 苏煌城,《奇异摄动问题中的边界层校正法》,科技出版社,上海(1983) [3] Илыин А.М.,Разностная смеха для дифференциалъного уравнения с малым параметром при сташей производной Мамеи.Замемкц,6,2(1969)237-248 [4] ЗЛамал М,(М.Zlamâl),О смешапной зацача цля оцного гнперболичсского уравненияс малым параметром,Чехол.Мам.Ж.,9(84)(1959),218-242 [5] Doolan,E.P.,J.J.H.Meller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980). [6] 苏煜城、吴启光,《微偏分方程数值解法》,南京大学数学系计算数学专业编,科学出版让(1979). -
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