Some Application for a Fuzzy Differential Equation and Solve by Runge-Kutta Method
DOI:
https://doi.org/10.62383/bilangan.v2i4.206Keywords:
Fuzzy differential equation, Modified two-step Simpson method, Runge-Kutta method, Initial value problemAbstract
In this article, the starting condition was defined using a fuzzy initial value problem (IVP). Additionally, we discussed various methods for solving fuzzy differential equations, including the modified two-step Simpson method and Runge-Kutta of orders (two, three, four, five, and six). For each method, we provided a numerical example and the known convergence rates of the solutions. Then we discussed the comparison of the solutions of all methods, using computer software to offer rough solutions for the Runge Kutta method. And take some application solve by Runge-Kutta in physics and medical
Downloads
References
Abbasbandy, S., & Viranloo, T. A. (2002). Numerical solution of fuzzy differential equation. Mathematical and Computational Applications, 7(1), 41-52. https://doi.org/10.3390/mca7010041
Allahviranloo, T., Ahmady, E., & Ahmady, N. (2008). Nth-order fuzzy linear differential equations. Information Sciences, 178(5), 1309-1324. https://doi.org/10.1016/j.ins.2007.10.013
Allahviranloo, T., Ahmady, N., & Ahmady, E. (2007). Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences, 177(7), 1633-1647. https://doi.org/10.1016/j.ins.2006.09.015
Barkhordari Ahmadi, M., & Khezerloo, M. (2011). Fuzzy bivariate Chebyshev method for solving fuzzy Volterra-Fredholm integral equations. International Journal of Industrial Mathematics, 3(2), 67-77.
Dhayabaran, D. P., & Kingston, J. C. (2016). Solving fuzzy differential equations using Runge-Kutta second order method for two stages contra-harmonic mean. International Journal of Engineering Science and Innovative Technology, 5(1), 154-161.
Dhayabaran, D. P., & Kingston, J. C. (2016). Solving fuzzy differential equations using Runge-Kutta third order method with modified contra-harmonic mean weights. International Journal of Engineering Research and General Science, 4(1), 292-300.
Fard, O. S., & Bidgoli, T. A. (2011). The Nyström method for hybrid fuzzy differential equation IVPs. Journal of King Saud University-Science, 23(4), 371-379. https://doi.org/10.1016/j.jksus.2010.07.020
Ghayyib, M. N., Fuleih, A. I., & Adnan, F. A. (2023). A statistical analysis of the effects of afforestation on the environment in Iraq (Northern Iraq). IOP Conference Series: Earth and Environmental Science, 1215(1), 012039. https://doi.org/10.1088/1755-1315/1215/1/012039
Ghazanfari, B., & Shakerami, A. (2012). Numerical solutions of fuzzy differential equations by extended Runge-Kutta-like formulae of order 4. Fuzzy Sets and Systems, 189(1), 74-91. https://doi.org/10.1016/j.fss.2011.06.018
Jayakumar, T., Maheskumar, D., & Kanagarajan, K. (2012). Numerical solution of fuzzy differential equations by Runge-Kutta method of order five. Applied Mathematical Sciences, 6(60), 2989-3002.
Jehad, R. K., & Manar, N. G. (2019). Properties of a general fuzzy normed space. Iraqi Journal of Science, 60(4), 847-855. https://doi.org/10.24996/ijs.2019.60.4.18
Jehad, R. K., & Manar, N. G. (2019). Properties of the space GFB(V, U). Journal of AL-Qadisiyah for Computer Science and Mathematics, 11(1). https://doi.org/10.29304/jqcm.2019.11.1.478
Jehad, R. K., & Manar, N. G. (2021). Properties of the adjoint operator of a general fuzzy bounded operator. BSJ, 18(1). https://doi.org/10.21123/bsj.2021.18.1(Suppl.).0790
Kaleva, O. (1987). Fuzzy differential equations. Fuzzy Sets and Systems, 24(3), 301-317. https://doi.org/10.1016/0165-0114(87)90029-7
Kaleva, O. (1990). The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems, 35(3), 389-396. https://doi.org/10.1016/0165-0114(90)90010-4
Khaki, M., & Ganji, D. D. (2010). Analytical solutions of nano boundary layer flows by using He's homotopy perturbation method. Mathematical and Computational Applications, 15(5), 962-966. https://doi.org/10.3390/mca15050962
Kim, H., & Sakthivel, R. (2012). Numerical solution of hybrid fuzzy differential equations using improved predictor-corrector method. Communications in Nonlinear Science and Numerical Simulation, 17(10), 3788-3794. https://doi.org/10.1016/j.cnsns.2012.02.003
Ma, M., Friedman, M., & Kandel, A. (1999). Numerical solutions of fuzzy differential equations. Fuzzy Sets and Systems, 105(1), 133-138. https://doi.org/10.1016/S0165-0114(97)00233-9
Malinowski, M. T. (2010). Existence theorems for solutions to random fuzzy differential equations. Nonlinear Analysis: Theory, Methods and Applications, 73(6), 1515-1532. https://doi.org/10.1016/j.na.2010.04.049
Radhy, Z. H., Maghool, F. H., & Abed, A. R. (2017). Numerical solution of fuzzy differential equation (FDE). International Journal of Mathematics Trends and Technology, 52(9), 596-602. https://doi.org/10.14445/22315373/IJMTT-V52P585
Raja, N., & Suganya, K. (2018). Numerical solution of fuzzy differential equation by comparison of Runge-Kutta sixth order method and Adam’s fifth order predictor-corrector method. International Journal of Science and Engineering Development Research, 3(7), 176-181.
Salahshour, S., Allahviranloo, T., & Abbasbandy, S. (2012). Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Communications in Nonlinear Science and Numerical Simulation, 17(3), 1372-1381. https://doi.org/10.1016/j.cnsns.2011.07.005
Salahshour, S., Allahviranloo, T., Abbasbandy, S., & Baleanu, D. (2012). Existence and uniqueness results for fractional differential equations with uncertainty. Advances in Difference Equations, 2012(1), 1-12. https://doi.org/10.1186/1687-1847-2012-112
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Ziari, S., Ezzati, R., & Abbasbandy, S. (2012). Numerical solution of linear fuzzy Fredholm integral equations of the second kind using fuzzy Haar wavelet. In Advances in Computational Intelligence (pp. 79-89). Berlin, Heidelberg.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.