Abstract
The main goal of this paper is to generalize the results, obtained in [1] to the case of quasi-linear ordinary differential equations of the second order with the third kind boundary conditions. It is a continuation of the paper series in which we have obtained weight a priori estimates of accuracy for difference schemes for linear parabolic type equations in one-dimensional [2] and two-dimensional [3] cases, quasi-linear parabolic type equations [4] and quasi-linear elliptic equations with conditions of the first kind [5]. In this paper it is shown that on approaching to the left or right boundary of the domain the rate of convergence of solution or it’s first derivative, correspondingly, increases. The second accuracy order difference scheme of the special form has been used for this purpose.
The paper is completed by numerical experiment, which results confirm theoretical statements.
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References
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Makarov, V.L., Demkiv, L.I.: Accuracy estimates of the difference schemes for parabolic type equations taking into account initial-boundary effect. Dopov. Nats. Akad. Nauk Ukr. 2, 26–32 (2003) (in Ukrainian)
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Makarov, V.L., Demkiv, L.I.: Accuracy estimates of the difference schemes for quasilinear parabolic equations taking into account the initial-boundary effect. Computational methods in applied mathematics 3(4), 579–595 (2003)
Makarov, V.L., Demkiv, L.I.: Accuracy Estimates of Difference Schemes for Quasi- Linear Elliptic Equations with Variable Coefficients Taking into Account Boundary Effect. In: Li, Z., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2004. LNCS, vol. 3401, pp. 80–90. Springer, Heidelberg (2005)
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Makarov, V.L., Demkiv, L.I. (2006). Taking into Account the Third Kind Conditions in Weight Estimates for Difference Schemes. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_79
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DOI: https://doi.org/10.1007/11666806_79
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