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The numerical solution of the second kind of Abel equations by the modified matrix-exponential method | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 11، دوره 14، شماره 12، اسفند 2023، صفحه 139-144 اصل مقاله (444.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29342.4131 | ||
| نویسندگان | ||
| Mohammad Fattahi* ؛ Mashallah Matinfar | ||
| Department of Mathematics, Science of Mathematics Faculty, University of Mazandaran, Babolsar, Iran | ||
| تاریخ دریافت: 25 آذر 1401، تاریخ بازنگری: 30 دی 1400، تاریخ پذیرش: 25 بهمن 1401 | ||
| چکیده | ||
| In this paper, the modified matrix exponential method (MME), under the zero-order hold (ZOH) assumption, is applied to solve the Abel equation of the second kind. The modified exponential matrix method is iterative, and by increasing the iteration, we can get a better approximation with fewer errors. We use the MME to turn an Abel differential equation into a system of nonlinear equations and determine the solution. By using the MME, the Abel differential equations approximate well. Using the numerical results, we can conclude that this method is effective, and in comparison with well-known techniques, the MME is highly accurate. | ||
| کلیدواژهها | ||
| Modified matrix exponential؛ Matrix exponential؛ Abel equation of the second kind؛ Nonlinear differential equations؛ Jacobian matrix | ||
| مراجع | ||
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[1] K.I. Al-Dosary, N.K. Al-Jubouri and H.K. Abdullah, On the solution of Abel differential equation by Adomian decomposition method, Appl. Math. Comput. 2 (2008), 2105–2118. [2] F. Allffi-Pentini, V. De Fonzo and V. Parisi, A novel algorithm for the numerical integration of systems of ordinary differential equations arising in chemical problems, J. Math. Chem. 33 (2003), no. 1, 1–15. [3] G. Alobaidi and R. Mailler, On the Abel equation of the second kind with sinusoidal forcing, Nonlinear Anal. Control 12 (2007), 33–44. [4] M.E. Fettis, On the numerical solution of equations of the Abel type, Math. Comput. 18 (1964), 491–496. [5] C. Guler and I. Parker, A new numerical algorithm for the Abel equation of the second kind, Int. J. Comput. Math. 84 (2007), no. 1, 109–119. [6] M. Gulsu, Y. Ozturk and M. Sezer, On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials, Appl. Math. Comput. 217 (2011), 4827–4833. [7] P. Hall, R. Paige and F.H. Ruymagaart, Using wavelet methods to solve noisy Abel-type equations with discontinuous inputs, J. Multivar. Anal. 86 (2003), 72–96. [8] T. Harko and M. Mak, Relativistic dissipative cosmological models and Abel differential equations, Comput. Math. Appl. 46 (2003), 849–853. [9] J. Lebrun, On two coupled Abel-type differential equations arising in a magnetostatic problem, Il Nuovo Cimento A (1965-1970) 103 (1990), no. 10, 1369–1379. [10] S. Mukherjee, D. Goswami and B. Roy, solution of higher-order Abel equations by differential transform method, Int. J. Modern Phys. C. 23 (2012). [11] J.M. Olm, X. Ros-Oton and Y.B. Shtessel, Stable Inversion of Abel equation: applications to tracking control in DC–DC nonlinear phase boost converters, J. Autom. 47 (2017), no. 1, 221–226. [12] Y. Park and K.T. Chong, The numerical solution of the point kinetics equation using the matrix exponential method, Ann. Nuclear Energy 55 (2013), 42–48. [13] R. Piessens and P. Verbaeten, Numerical solution of the Abel integral equation, BIT 13 (1973), 451–457. [14] Z. Zhang, D.U. An, H.S. Kim and K.T. Chong, Comparative study of matrix exponential and Taylor series discretization methods for nonlinear ODEs, Simul. Model. Practice Theory 17 (2009), 471–484. | ||
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