奇异摄动偏微分方程的周期边界问题<sup>*</sup>

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奇异摄动偏微分方程的周期边界问题^*

基金项目: * 国家自然科学基金;福建省自然科学基金

摘要: 本文讨论奇异摄动椭圆抛物型偏微分方程的周期边界问题.构造一个差分格式,利用分离解的奇性项的方法,结合问题的渐近展开,证明所构造的差分格式具有O(τ+h²)一致收敛阶.
- 椭圆抛物型偏微分方程 /
- 奇异摄动问题 /
- 周期边界 /
- 差分格式 /
- 一致收敛性
Abstract: In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h²).
- elliptic-parabolic partial differential equation /
- singular perturbation problem /
- periodic boundary /
- difference scheme /
- uniform convergence

[1]	Печенкина А А.,Решение периодической задачи дпя обыкновеннного дифферендиалного урлвнения второго поряцкэ с малым лбранетром при сторшей проиеводиой,Дцфференццальные У раэнеия с Малым Парамемром,Сверддовск(1980) 111-1118
[2]	林鹏程、江本话,奇异摄动的周期边界问题,应用数学和力学,8(1987),877-893
[3]	Kellogg,R.B.and A.Tsan,Analysis of some difference approximations for a singular perturbation problem without turning points,Math.Comp.,32(1987),1025-1039.
[4]	Il'in,A.M.,Difference scheme for a differential equation with a small parameter affecting the highest derivative,Mat.Zametki.,6(1969),237-248.
[5]	Емелъянов К.В.,О Разностной методе решения третъей краевой задачи для дифферендиалъного Уравнения с малым параметром при старшей производной,Ж.Бычисл Мамем.Физики,15,6(1975),1455-1463
[6]	苏煜城,外推法对奇异摄动问题数值解的应用,应用数学和力学,6,4 (1985),289-302