Chen Ming-lun, Wang Guo-ying. Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point[J]. Applied Mathematics and Mechanics, 1990, 11(1): 67-77.
Citation: Chen Ming-lun, Wang Guo-ying. Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point[J]. Applied Mathematics and Mechanics, 1990, 11(1): 67-77.

Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point

  • Received Date: 1988-05-05
  • Publish Date: 1990-01-15
  • In this paper we construct a completely exponentially fitted finite difference scheme for the boundary value problem of differential equation with turning points, extending Miller's method[1] and simplifying the method of the proof. We prove the first order uniform convergence of the scheme. The numerical results show that it is better than Il'in's scheme.
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    Carroll,J.and J.J.H.Miller,Completely exponentially fitted finite difference schemes for some singular perturbation problems,boundary and interior layers,Computational and Asymptotic Methods,Ed.J.J.H.Miller,Boole Press,Dublin(1980),225-230.
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    Il'in,A.M.,Differencing scheme for a differetial equation with a small parameter affecting the highest derivative,Math.Notes Acad.Sci.,USSR.6(1969),596-602.
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    Miller,J.J.H.,Sufficient conditions for the convergence uniformly in ε,of a three-point difference scheme for a singular perturbation problem,Proc.Oberwolfach,Germany,Lecture Notes in Maths.,Springer-Verlag,679(1977),85-91.
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    Kellogg,R.B.,Difference approximation for a singular perturbation problem with turning points,Analysis and numerical approaches to asymptotic problems in analysis,S.Axelsson,L.S.Frank,V.Slusis(eds),North-Holland Publishing Company(1981),133-139.
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    Lakin,W.D.,Foundary value problems with a turning point,Studies in Appl.Math.,51,3(1972),261-275.
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    O'Malley,R.E.,Introdution Singular Perturbations,Acad.Press,New York and London(1974).
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    Cook,L.P.and W.Eckhaus,Resonance in boundary value problem of singular perturbation type,Studies in Appl.Math.,52,2(1973),129-139.
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    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).
    [12]
    Kellogg,R.B.and A.Tsan,Analysis of some difference approximations for a singular perturbation problem without turning point,Math.Comp.,32(1978),1025-1039.
    [13]
    Jiang Fu-ru,On the boundary value problems for a class of ordinary differential equations with turning points,Appl.Math and Mech.,1,2(1980),201-213.
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