آمار
| تعداد نشریات | 43 |
| تعداد شمارهها | 1,230 |
| تعداد مقالات | 15,135 |
| تعداد مشاهده مقاله | 50,655,233 |
| تعداد دریافت فایل اصل مقاله | 13,743,844 |
Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 9، دوره 9، شماره 3، مهر 2021، صفحه 762-773 اصل مقاله (381.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.35252.1604 | ||
| نویسندگان | ||
| Shabnam Paseban Hag1؛ Elnaz Osgooei* 1؛ Elmira Ashpazzadeh2 | ||
| 1Faculty of Science, Urmia University of Technology, Urmia, Iran. | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. | ||
| چکیده | ||
| In this paper, we first construct Alpert wavelet system and propose a computational method for solving a fractional nonlinear Fredholm integro-differential equation. Then we create an operational matrix of fractional integration and use it to simplify the equation to a system of algebraic equations. By using Newtons iterative method, this system is solved and the solution of the fractional nonlinear Fredholm integro-differential equations is achieved. Thresholding parameter is used to increase the sparsity of matrix coefficients and the speed of computations. Finally, the method is demonstrated by examples, and then compared results with CAS wavelet method show that our proposed method is more effective and accurate. | ||
| کلیدواژهها | ||
| Alpert wavelet system؛ Fredholm integro-differential equation؛ Operational matrix؛ Fractional equation | ||
| مراجع | ||
|
[1] C. Allouch, P. Sablonniere, D. Sbibih, and M. Tahrichi, Product integration methods based on discrete spline quasi interpolants and application to weakly singular integral equations. Comput. Appl. Math., 233 (2010), 2855–66. [2] B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, Wavelet-like bases for the fast solution of second kind integral equations, SIAM J. Sci. Comput., 14 (1993), 159–84. [3] E. Babolian and F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput. 188 (2007), 417–26. [4] M. Dehghan B. Nemati Saray, and M. Lakestani, Three methods based on the interpolation scaling functions and the mixed collocation finite difference schemes for the numerical solution of the nonlinear generalized Burgers-Huxley equation, Math. Comput. Modeling, 55 (2012), 1129–42. [5] JH. He, Nonlinear oscillation with fractional derivative and its applications. In: International conference on vibrating engineering 98. China: Dalian; (1998), 288–91. [6] JH. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15 (1999), 86–90. [7] CH. Wu SP. Hsiao, Numerical solution of time-varying functional differential equations via Haar wavelets, Appl. Math. Comput. 188 (2007), 1049–58. [8] M. Ilie, J. Biazar, and Z. Ayati, Neumann method for solving conformable fractional Volterra integral equations, Comput. Methods Differ. Equ., 8(1) (2020), 54–68. [9] S. Irandoust-pakchin, M. Dehghan, and S. Abdi-mazraeh, Numerical solution for a class of fractional convection diffusion equations using the flatlet oblique multiwavelets, JVC/Journal of Vibration and Control., 20 (2014), 913–924. [10] M. Lakestani, B. Nemati Saray, and M. Dehghan, Numerical solution for the weakly singular Fredholm integro differential equations using Legendre multiwavelets, J. Comput. Appl. Math., 235 (2011), 3291-3303. [11] K. Maleknejad and S. Sohrabi, Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets, Appl. Math. Comput., 186 (2007), 836–43. [12] B. Mandelbrot, Some noises with 1f spectrum, a bridge between direct current and white noise, IEEE. Trans. Inform. Theory., 13 (1967), 289–298. [13] S. Momani and MA. Aslam Noor, Numerical methods for fourth-order fractional integrodifferential equations, Appl. Math. Comput., 182 (2006), 754–760. [14] Y. Nawaz, Variational iteration method and homotopy perturbaion method for fourth-order fractional integro differential equations, Comput. Math. Appl., 61 (2011), 2330–2341. [15] B. Nemati Saray, M. Lakestani, and M. Razzaghi, Sparse representation of system of Fredholm integro-differential equations by using alpert multiwavelets, Comput. Math. Math. Phys., 55 (2015), 1468–1483. [16] P. Rahimkhani, Y. Ordokhani, and E. Babolian, Fractional-order Bernoulli functions and their applications in solving fractional FredholemVolterra integro-differential equations, Appl. Numer. Math., 122 (2017), 66–81. [17] P. Rahimkhani, Y. Ordokhani, and E. Babolian, Mntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations, Numer. Algorithms., 77 (2018), 1283–1305. [18] M. Razzaghi and Y. A. Ordokhani, rationalized Haar functions method for nonlinear FredholmHammerstein integral equations, Int. J. Comput. Math., 79 (2002), 333–343. [19] R. Panda and M. Dash, Fractional generalized splines and signal processing, Signal Process., 86 (2006), 2340–2350. [20] SS. Ray, Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method, Commun. Nonlinear. Sci. Numer. Simulat., 14 (2009), 1295–306. [21] YA. Rossikhin and MV. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary machines of solids, Appl. Mech. Rev., 50 (1997) 15–67. [22] S. Sabermahani, Y. Ordokhani, and S. A. Yousefi, Fractional-order general Lagrange scaling functions and their applications, Bit Numer Math 60., (2019), 101–128. [23] H. Saeedi, MM. Moghadam, N. Mollahasani, and GN. Chuev, A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order, Commun. Nonlinear. Sci. Numer. Simulat., 16 (2011), 1154–63. [24] V. E. Tarasov, Fractional vector calculus and fractional Maxwells equations, J. Ann. Physics., 323 (2008), 2756–2778. [25] S. Yousefi and A. Banifatemi, Numerical solution of Fredholm integral equations by using CAS wavelets, Appl. Math. Comput., 183 (2006), 458–463. [26] S. Yousefi and M. Razzaghi, Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations, Math. Comput. Simulation., 70 (2005), 1–8. [27] L. Zhu and Q. Fan, Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet, Commun. Nonlinear. Sci. Numer. Simulat., 17 (2012), 2333–2341. | ||
|
آمار تعداد مشاهده مقاله: 393 تعداد دریافت فایل اصل مقاله: 304 |
||