Abstract
In this paper, we consider a second order ordinary differential equation with a small, positive parameter ε in its highest derivative for periodic boundary values problem and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.
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Pejinkina, A.A., Solution of the period problem for second order ordinary differential equation with small parameter in its leading derivatives.Differential Equations with Small Parameter (1980), 111–118. (in Russian)
Emelyanov, K.V., A difference method for solving the third boundary problem for a differential equation with small parameter in its leading derivatives,USSR Computational Math. and Math. Phys.,15, 6 (1975), 1455–1463. (in Russian)
II’in, A.M., Differece schemes for a differential equation with a small parameter affecting the highest derivativeMat. Zametki,6 (1969), 237–248.
Kellogg, R.B. and A. Tsan, Analysis of some difference approximation for a singular perturbation problem without turning points,Math. Comp.,32 (1978), 1025–1039.
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Communicated by Lin Zong-chi
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Peng-cheng, L., Ben-xian, J. A singular perturbation problem for periodic boundary differential equation. Appl Math Mech 8, 929–937 (1987). https://doi.org/10.1007/BF02454255
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DOI: https://doi.org/10.1007/BF02454255