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F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 2، دوره 14، شماره 6، زمستان 2017، صفحه 1-13 اصل مقاله (323 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3495 | ||
| نویسندگان | ||
Irina Perfilieva  1؛ Petra Stevuliakova2؛ Radek Valasek1
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| 1University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic | ||
| 2University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic | ||
| چکیده | ||
| We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems. | ||
| کلیدواژه‌ها | ||
| F-transform؛ Differential equation؛ Boundary value problem؛ Second order differential equation | ||
| مراجع | ||
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[1] V. I. Arnold and R. Cook, Ordinary Diff erential Equations, Springer Textbook, Springer, Berlin Heidelberg, 1992. ISBN 9783540548133. [2] U. Ascher, Collocation for two-point boundary value problems revisited, SIAM J. Numer. Anal. 23 (1986), 596{609. [3] K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed., John Wiley, Iowa, USA, 1988. [4] N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobelkov, Numerical Methods, Nauka, Moskva, (1987), 600 p. [5] W. Chen and Y. Schen, Approximate solution for a class of second-order ordinary diff erenci- tal equations by the fuzzy transform, Intelligent and Fuzzy Systems. 27 (2014), 73{82. [6] H. Keller, Numerical Methods for Two-Point Boundary Value Problems, Ginn (Blaisdell), Boston, 1968. [7] A. Khastan, I. Perfi lieva and Z. Alijani, A new fuzzy approximation method to Cauchy prob- lems by fuzzy transform, Fuzzy Sets and Systems, 288 (2016), 75{95. [8] A. Khastan, Z. Alijani and I. Perfi lieva, Fuzzy transform to approximate solution of two- point boundary value problems, Mathematical Methods in the Applied Sciences. (2016), http://dx.doi.org/10.1002/mma.3832. [9] I. Perfi lieva, Fuzzy transforms: Theory and applications, Fuzzy Sets and Systems, 157 (2006), 993{1023. [10] I. Perfi lieva, Fuzzy approach to solution of diff erential equations with imprecise data: appli- cation to reef growth problem, in: R.V. Demicco, G.J. Klir (Eds.), Fuzzy Logic in Geology, Academic Press, Amsterdam, (2003), 275-300. [11] I. Perfi lieva, M. Holcapek and V. Kreinovich, A new reconstruction from the F-transform components, Fuzzy Sets and Systems, 288 (2016), 3{25. [12] A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, Springer, New York, 2007. [13] P. Stevuliakova, I. Perfi lieva and R. Valasek, R., A New Approach to Fuzzy Boundary Value Problem, in: World Scientifi c Proceedings Series on Computer Engineering and Information Science, 10 (2016), 276{281. | ||
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