A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem

G. M. Amiraliyev; Hakk Duru

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(4): 363-370

G. M. Amiraliyev, Hakk Duru. A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem[J]. Applied Mathematics and Mechanics, 1999, 20(4): 363-370.

Citation:

G. M. Amiraliyev, Hakk Duru. A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem[J]. Applied Mathematics and Mechanics, 1999, 20(4): 363-370.

Citation:

G. M. Amiraliyev, Hakk Duru. A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem[J]. Applied Mathematics and Mechanics, 1999, 20(4): 363-370.

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A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem

Deptartment of Mathematics, Y Y University, 65080 VAN, TURKEY

Received Date: 1997-11-25
Publish Date: 1999-04-15

Abstract

Abstract

Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered.An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh,which gives first-order uniform convergence in the sense of discrete maximum norm.Numerical results are also presented.
- singular perturbation,
- difference scheme,
- uniform convergence,
- initial value condition,
- linear ordinary differential equation

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References(10)

References

[1]	O' Malley R E,Jr.Introduction to Singular Perturbations[M].New York:Academic Press,1974.
[2]	O'Malley R E,Jr.Singular Perturbation Methods for Ordinary Differential Equations[M].New York:Springer-Verlag,1991.
[3]	Neyfeh A H.Perturbation Methods[M].Wiley,1973.
[4]	苏煜城,林平.具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式[J].应用数学和力学,1990,11(4):283~294.
[5]	Boglaev I P.Numerical integration of an initial value problems for a systems with a small parameter affecting the derivative[J].USSR Comput Math Mac Pys,1987,27:63~75.(in Russian)
[6]	Doolan E P,Miller J J H,Schilders W H A.Uniform Numerical Methods for Problems with Initial and Boundary Layers[M].Dublin:Boole Press,1980.
[7]	Amiraliyev G M.Difference schemes on the uniform mesh for singular perturbed pseudo-parabolic equations[J].Turkish J Math,1995,19:207~222.
[8]	Amiraligev G M.On difference schemes for problems of the theory of dispersive waves[J].Soviet Math Dokl,1991,42:235~238.
[9]	Amiraliyev G M.Difference method for the solution of one problem of the theory dispersive waves[J].Differential Equations,1990,26:2146~2154.(in Russian)
[10]	Samarski A A.Theory of Difference Schemes[M].2nd Ed.Moscow:“Nauka”,1983;German transl,Leibzig:Geest Portig,1984.