Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems

Yin Guang-yan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1986 > 7(4): 343-352

Yin Guang-yan. Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems[J]. Applied Mathematics and Mechanics, 1986, 7(4): 343-352.

Citation:

Yin Guang-yan. Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems[J]. Applied Mathematics and Mechanics, 1986, 7(4): 343-352.

Citation:

Yin Guang-yan. Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems[J]. Applied Mathematics and Mechanics, 1986, 7(4): 343-352.

PDF( 602 KB)

Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems

Yin Guang-yan

Jiangnan University Jiangsu

Received Date: 1985-01-25
Publish Date: 1986-04-15

Abstract

Abstract

A difference scheme is established in this paper for second-order hyperbolic-hyperbolic singular perturbation mixed problems.We give an energy inequality of the numerical solution and prove that the numerical solution converges to the solution of the singular perturbation problems uniformly with respect to a small parameter and in the sense of a discrete norm.

FullText(HTML)

References(10)

References

[1]	Genet,J,Monique Madaune,Singular perturbations for a class of nonlinear hyperbolichyperbolic problems,Jour.Math.Anal.Appl,64(1978),1-24.
[2]	de Jager,E.M.,Singular perturbations of hyperbolic type,Analytical and Numerical Approaches to Asymptotic Problems in Analysis,S.Axclsson,L.S.Frank,A.Van der Sluis(eds.),North-Holland Publishing Company(1981).
[3]	苏煜城,二阶拟线性双曲型方程奇异摄动柯西问题的渐近解,高等学校计算数学学报,1(1979),80-91.
[4]	苏煜城,二阶拟线性双曲型方程奇异摄动混合问题的渐近解,南京大学学报1(1980),19-29.
[5]	Зламал М.,Осмешанной задаче для одного гинперблическок уравнения с иалым параметром,Чехословацкцй Мамемцческцй Журнал,84,9(1959),218-242.
[6]	张伟江、马晓云,双曲型偏微分方程寄异摄动问题的差分解法,上海交通大学学报,1(1983).
[7]	苏煜城,《奇异摄动中的边界层校正法》,上海科学技术出版社(l983).
[8]	Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980).
[9]	戈杜诺夫C,K,,B,C.李亚宾基,《差分格式理论导引》(中译本),冯果忱等译,上海科李技术出版社(1966).
[10]	苏煜城、吴启光,《偏微分方程数值解法》,科学出版社(1979).