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Soft Computing

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15.07.2016 | Methodologies and Application

Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

verfasst von: Omar Abu Arqub, Mohammed Al-Smadi, Shaher Momani, Tasawar Hayat

Erschienen in: Soft Computing | Ausgabe 23/2017

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Abstract

In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation in the space \(\oplus _{j=1}^2 W_2^3 \left[ {a,b}\right] \). An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.

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Abu Arqub O (2015) Adaptation of reproducing Kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl. doi:10.1007/s00521-015-2110-x

Abu Arqub O (2016) The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations. Math Method Appl Sci. doi:10.1002/mma.3884 MATH

Abu Arqub O, Al-Smadi M (2014) Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations. Appl Math Comput 243:911–922. doi:10.1016/j.amc.2014.06.063 MATHMathSciNet

Abu Arqub O, Al-Smadi M, Shawagfeh N (2013) Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method. Appl Math Comput 219:8938–8948. doi:10.1016/j.amc.2013.03.006 MATHMathSciNet

Abu Arqub O, El-Ajou A, Momani S, Shawagfeh N (2013b) Analytical solutions of fuzzy initial value problems by HAM. Appl Math Inf Sci. 7:1903–1919. doi:10.12785/amis/070528 CrossRefMathSciNet

Abu Arqub O, Momani S, Al-Mezel S, Kutbi M (2015a) Numerical solutions of fuzzy differential equations using reporducing kernel Hilbert space mehtod. Soft Comput. doi:10.1007/s00500-015-1707-4 MATH

Abu Arqub O, Momani S, Al-Mezel S, Kutbi M (2015) Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type. Math Probl Eng. doi:10.1155/2015/835891 MATHMathSciNet

Al-Smadi M, Abu Arqub O, Shawagfeh N, Momani S (2016) Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method. Appl Math Comput. In Press

Bede B (2006) A note on “two-point boundary value problems associated with non-linear fuzzy differential equations”. Fuzzy Sets Syst 157:986–989. doi:10.1016/j.fss.2005.09.006 CrossRefMATHMathSciNet

Bede B, Gal SG (2004) Almost periodic fuzzy-number-valued functions. Fuzzy Sets Syst 147:385–403. doi:10.1016/j.fss.2003.08.004 CrossRefMATHMathSciNet

Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581–599. doi:10.1016/j.fss.2004.08.001 CrossRefMATH

Berlinet A, Agnan CT (2004) Reproducing kernel Hilbert space in probability and statistics. Kluwer Academic Publishers, Boston. doi:10.1007/978-1-4419-9096-9 MATH

Chalco-Cano Y, Román-Flores H (2008) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 38:112–119. doi:10.1016/j.chaos.2006.10.043 CrossRefMATHMathSciNet

Chen M, Fu Y, Xue X, Wu C (2008) Two-point boundary value problems of undamped uncertain dynamical systems. Fuzzy Sets Syst 159:2077–2089. doi:10.1016/j.fss.2008.03.006 CrossRefMATHMathSciNet

Chen M, Wu C, Xue X, Liu G (2008b) On fuzzy boundary value problems. Inf Sci 178:1877–1892. doi:10.1016/j.ins.2007.11.017 CrossRefMATHMathSciNet

Cherki A, Plessis G, Lallemand B, Tison T, Level P (2000) Fuzzy behavior of mechanical systems with uncertain boundary conditions. Comput Methods Appl Mech Eng 189:863–873. doi:10.1016/S0045-7825(99)00401-6 CrossRefMATH

Cui M, Lin Y (2009) Nonlinear numerical analysis in the reproducing kernel space. Nova Science, New YorkMATH

Daniel A (2003) Reproducing kernel spaces and applications. Springer, Basel. doi:10.1007/978-3-0348-8077-0 MATH

Gasilov N, Amrahov E, Fatullayev AG (2014) Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst 257:169–183. doi:10.1016/j.fss.2013.08.008 CrossRefMATHMathSciNet

Gasilov N, Amrahov E, Fatullayev AG, Hashimoglu IF (2015) Solution method for a boundary value problem with fuzzy forcing function. Inf Sci 317:349–368. doi:10.1016/j.ins.2015.05.002

Geng F, Qian SP, Li S (2014) A numerical method for singularly perturbed turning point problems with an interior layer. J Comput Appl Math 255:97–105. doi:10.1016/j.cam.2013.04.040

Geng F, Cui M (2012) A reproducing kernel method for solving nonlocal fractional boundary value problems. Appl Math Lett 25:818–823. doi:10.1016/j.aml.2011.10.025 CrossRefMATHMathSciNet

Geng F, Qian SP (2013) Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers. Appl Math Lett 26:998–1004. doi:10.1016/j.aml.2013.05.006 CrossRefMATHMathSciNet

Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43. doi:10.1016/0165-0114(86)90026-6

Guo X, Shang D, Lu X (2013) Fuzzy approximate solutions of second-order fuzzy linear boundary value problems. Bound Value Probl. doi:10.1186/1687-2770-2013-212 MATHMathSciNet

Hüllermeier E (1997) An approach to modelling and simulation of uncertain systems. Int J Uncertain Fuzziness Knowl Based Syst 5:117–137. doi:10.1142/S0218488597000117 CrossRefMATHMathSciNet

Jiang W, Chen Z (2013) Solving a system of linear Volterra integral equations using the new reproducing kernel method. Appl Math Comput 219:10225–10230. doi:10.1016/j.amc.2013.03.123 MATHMathSciNet

Jiang W, Chen Z (2014) A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation. Numer Methods Partial Differ Equ 30:289–300. doi:10.1002/num.21809 CrossRefMATHMathSciNet

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317. doi:10.1016/0165-0114(87)90029-7 CrossRefMATHMathSciNet

Khastan A, Bahrami F, Ivaz K (2009) New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability. Bound Value Probl. doi:10.1155/2009/395714 MATH

Khastan A, Nieto JJ (2010) A boundary value problem for second order fuzzy differential equations. Nonlinear Anal 72:3583–3593. doi:10.1016/j.na.2009.12.038 CrossRefMATHMathSciNet

Lakshmikantham V, Murty KN, Turner J (2001) Two-point boundary value problems associated with non-linear fuzzy differential equations. Math Inequal Appl 4:527–533. doi:10.7153/mia-04-47 MATHMathSciNet

Li C, Cui M (2003) The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Appl Math Comput 143:393–399. doi:10.1016/S0096-3003(02)00370-3 MATHMathSciNet

Li D, Chen M, Xue X (2011) Two-point boundary value problems of uncertain dynamical systems. Fuzzy Sets Syst 179:50–61. doi:10.1016/j.fss.2011.05.012 CrossRefMATHMathSciNet

Mohammadi M, Mokhtari R (2011) Solving the generalized regularized long wave equation on the basis of a reproducing kernel space. J Comput Appl Math 235:4003–4014CrossRefMATHMathSciNet

Momani S, Abu Arqub O, Hayat T, Al-Sulami H (2014) A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Voltera type. Appl Math Comput 240:229–239. doi:10.1016/j.amc.2014.04.057 MATHMathSciNet

Mosleh M, Otadi M (2015) Approximate solution of fuzzy differential equations under generalized differentiability. Appl Math Model 39:3003–3015. doi:10.1016/j.apm.2014.11.035 CrossRefMATHMathSciNet

Nieto JJ, Khastan A, Ivaz K (2009) Numerical solution of fuzzy differential equations under generalized differentiability. Nonlinear Anal Hybrid Syst 3:700–707. doi:10.1016/j.nahs.2009.06.013 CrossRefMATHMathSciNet

O’Regana D, Lakshmikantham V, Nieto JJ (2003) Initial and boundary value problems for fuzzy differential equations. Nonlinear Anal 54:405–415. doi:10.1016/S0362-546X(03)00097-X CrossRefMATHMathSciNet

Wang W, Cui M, Han B (2008) A new method for solving a class of singular two-point boundary value problems. Appl Math Comput 206:721–727. doi:10.1016/j.amc.2008.09.019 MATHMathSciNet

Titel: Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems
verfasst von: Omar Abu Arqub
Mohammed Al-Smadi
Shaher Momani
Tasawar Hayat
Publikationsdatum: 15.07.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 23/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-016-2262-3

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