آمار
| تعداد نشریات | 45 |
| تعداد شمارهها | 1,513 |
| تعداد مقالات | 18,499 |
| تعداد مشاهده مقاله | 60,462,011 |
| تعداد دریافت فایل اصل مقاله | 21,431,865 |
Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 15، دوره 9، شماره 3، مهر 2021، صفحه 846-857 اصل مقاله (354.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2021.22093.1257 | ||
| نویسندگان | ||
| Mohamed A. Ramadan1؛ Mohamed Reda Ali* 2 | ||
| 1Department of Mathematics, Faculty of Science, Menoua University, Egypt. | ||
| 2Department of Mathematics, Faculty of Engineering, Benha University, Egypt. | ||
| چکیده | ||
| In this paper, we have proposed an efficient numerical method to solve a system linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM). Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear Fredholm fuzzy integral equations. First, we introduce properties of Bernoulli wavelets then we used it to transform the integral equations to the system of algebraic equations, the error estimates of the proposed method are given and compared by solving some numerical examples. | ||
| کلیدواژهها | ||
| Parametric form of a Fuzzy number؛ Bernoulli wavelets؛ Fuzzy integral equations؛ Approximate solution؛ product matrix؛ Error estimation | ||
| مراجع | ||
|
[1] G. A. Anastassiou, Fuzzy Mathematics, Approximation Theory, Springer, CityplaceHeidelberg, 2010. [2] M. Barkhordari and M. Khezerloo, Fuzzy bivariate Chebyshev method for solving fuzzy Volterra– Fredholm integral equations, Int. J. Ind. Math, 3(2) (2011), 67–77. [3] R. Goetschel and W. Vaxman, Elementary calculus, Fuzzy Sets Syst, 18 (1986), 31–43. [4] O. Kaleva, Fuzzy differential equations, Fuzzy Sets Syst, 24 (1987), 301– 317. [5] O. Kouba, Lecture notes: Bernoulli polynomials and applications, 2013. [6] K. Maleknejad and H. Derili, Numerical solution of Hammerstein integral equations by using combination of spline collocation method and Lagrange interpolation, Appl. Math. Comput, 190 (2007), 1557–1562. [7] F. Mirzaee, M. Paripour, and M. Komak, Application of Triangular and Delta Basis Functions to Solve Linear Fredholm Fuzzy Integral Equation of the Second Kind, Arab J Sci Eng, 39 (2014), 3969–3978. [8] A. Molabahrami, A. Shidfar, and A. Ghyasi, An analytical method for solving linear Fredholm fuzzy integral equations of the second kind, Comput. Math. Appl, 61 (2011), 2754–2761. [9] M. Mosleh and M. Otadi, Solving a System of Fuzzy Integral Equations by an Analytic Method, Comput. Math. Appl, 3 (2015), 67-71. [10] H. T. Nguyen, A note on the extension principle for fuzzy sets, J.Math. Anal. Appl, 64 (1978), 369–380. [11] L. Pretorius and D. Eyre, Spline-Gauss rules and the Nystrm method for solving integral equations in quantum scattering, J. Comput. Appl. Math, 18 (1987), 235–247. [12] M. A. Ramadan and M. R. Ali, Numerical Solution of Volterra-Fredholm Integral Equations Using Hybrid Orthonormal Bernstein and Block-Pulse Functions, Asian Res. Journal. Math, 4 (2017), 1-14. [13] M. A. Ramadan and M. R. Ali, Solution of integral and Integro- Differential equations system using Hybrid orthonormal Bernstein and block-pulse functions, Journal. abst. Comput. Math, 2 (2017),35-48. [14] M. A. Ramadan and M. R. Ali, An efficient hybrid method for solving Fredholm integral equations using triangular functions, New Trends. Math Sciences, 5 (2017), 213-224. [15] M. A. Ramadan, T. S. El-Danaf, and A. M. E. Bayoumi, A finite iterative algorithm for the solution of Sylvester conjugate matrix equation AV + BW = EVF +Cand AV + BW = EVF+ C, Journal . Math. Comput. Modelling, 58 ( 2013), 1738–1754. [16] C. Wu and M. Ma, On the integrals, series and integral equations of fuzzy set-valued functions, J. Harbin Inst. Technol, 21 (1990), 11–19. | ||
|
آمار تعداد مشاهده مقاله: 730 تعداد دریافت فایل اصل مقاله: 525 |
||