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Vol.3 , No. 5, Publication Date: Dec. 6, 2017, Page: 36-43
| [1] | Erdem Uzun, Department of Physics, Karamanoğlu Mehmetbey University, Karaman, Turkey. |
One trap one recombination center model was proposed to explain thermoluminescence emission and it should be emphasized that the model has its own allowed charge carrier transitions, trapping parameters and differential equations set. The equations are not linear and thus analytical solutions are not possible. Therefore, numerical solutions of the thermoluminescence equations have been effectively used in thermoluminescence studies. In this paper the one trap one recombination center model is solved, numerically by using Explicit Euler, Generalized Euler, Classical Runge-Kutta, Implicit Runge-Kutta and Explicit Runge–Kutta methods for different step sizes and differential orders. In order to comparison of the simulations, some experiments are also performed. Moreover, experimental trap parameters are used as initial conditions in the simulations. Because working precision is held as many digits throughout the numerical solutions, very precise figure of merit values are calculated. Number of simulations show that when difference between the FOM values, which calculated by using various numerical methods, are very small, the shortness of calculation time seems to be a good criterion in the choice of method.
Keywords
Thermoluminescence, Otor Model, Numerical Solution, Runge-Kutta
Reference
| [01] | S. W. S. McKeever, Thermoluminescence of Solids, Cambridge University Press, Cambridge, 1985. doi: 10.1017/CBO9780511564994. |
| [02] | R. Chen, S. W. S. McKeever, Theory of Thermoluminescence and Related Phenomena, 1997. doi: 10.1142/2781. |
| [03] | R. Chen, V. Pagonis, Thermally and Optically Stimulated Luminescence: A Simulation Approach, 2011. doi: 10.1002/9781119993766. |
| [04] | P. J. Kemmey, P. D. Townsend, P. W. Levy, Numerical analysis of charge-redistribution processes involving trapping centers, Phys. Rev. 155 (1967) 917–920. doi: 10.1103/PhysRev.155.917. |
| [05] | P. Kelly, M. J. Laubitz, P. Bräunlich, Exact solutions of the kinetic equations governing thermally stimulated luminescence and conductivity, Phys. Rev. B. 4 (1971) 1960–1968. doi: 10.1103/PhysRevB.4.1960. |
| [06] | D. Shenker, R. Chen, Numerical solution of the glow curve differential equations, J. Comput. Phys. 10 (1972) 272–283. doi: 10.1016/0021-9991(72)90066-6. |
| [07] | R. Chen, W. F. Hornyak, V. K. Mathur, Competition between excitation and bleaching of thermoluminescence, J. Phys. D. Appl. Phys. 23 (1990) 724–728. doi: 10.1088/0022-3727/23/6/015. |
| [08] | H. G. Balian, N. W. Eddy, Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks, Nucl. Instruments Methods. 145 (1977) 389–395. doi: 10.1016/0029-554X(77)90437-2. |
| [09] | S. W. S. McKeever, Thermoluminescence of Solids:, Cambridge University Press, Cambridge, 1985. doi: 10.1017/CBO9780511564994. |
| [10] | J. D. Hoffman, Numerical Differentiation and Difference Formulas, in: Numer. Methods Eng. Sci., Second Edi, Marcel Dekker, Inc, NEW YORK. BASEL, 2001: pp. 257-270. |
| [11] | J. Bulirsch, R. Stoer, Ordinary Differential Equations, in: J. E. Marsden, M. Golubitsky, L. Sirovich, W. Jager (Eds.), Introd. to Numer. Anal., Second Edi, Springer-Verlag New York, Inc., New York, 1992: pp. 434-471. |
| [12] | W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Integration of Ordinary Differential Equations, in: W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery (Eds.), Numer. Recipes Fortran 77 Art Sci. Comput., Second Edi, Press Syndicate of the University of Cambridge, Cambridge, 1997: pp. 704-716. |
| [13] | S. D. Conte, C. de Boor, The Solution of Differential Equations, in: S. D. Conte, C. de Boor (Eds.), Elem. Numer. Anal. An Algorithmic Approach, Third Edit, McGraw-Hill, inc., New York, 1980: pp. 354-370. |
| [14] | L. F. Shampine, Some Practical Runge-Kutta Formulas, Math. Comput. 46 (1986) 135. doi: 10.2307/2008219. |
| [15] | E. Fehlberg, Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control, NASA Tech. Rep. (1968) R-287. doi: 10.1007/BF02234758. |
| [16] | P. Bogacki, L. Shampine, A 3 (2) Pair of Runge-Kutta Formulas, Appl Math Lett. 2 (1989) 321–325. doi: 10.1016/0893-9659(89)90079-7. |
| [17] | P. Bogacki, L. F. Shampine, An efficient Runge-Kutta (4, 5) pair, Comput. Math. with Appl. 32 (1996) 15–28. doi: 10.1016/0898-1221(96)00141-1. |
| [18] | J. Nearing, Mathematical Tools for Physics, Analysis. 30 (2003) 1316–22. doi: 10.1002/3527607773. |
| [19] | M. Sofroniou, R. Knapp, Advanced Numerical Differential Equation Solving in Mathematica, … Inc. URL Http//reference. Wolfram. Com/mathematica/ …. (2008). http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle: ADVANCED+NUMERICAL+DIFFERENTIAL+EQUATION+SOLVING+IN+MATHEMATICA#1. |
| [20] | M. Trott, The Mathematica GuideBook for Numerics, Springer New York, New York, NY, 2006. doi: 10.1007/0-387-28814-7. |
