پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 705 |
| تعداد مقالات | 10,155 |
| تعداد مشاهده مقاله | 71,516,246 |
| تعداد دریافت فایل اصل مقاله | 63,226,976 |
Numerical approach for reconstructing an unknown source function in inverse parabolic problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 43، دوره 12، شماره 1، مرداد 2021، صفحه 555-565 اصل مقاله (1.08 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4838 | ||
| نویسندگان | ||
| Javad Damirchi* 1؛ Ali Janmohammadi2؛ Masoud Hasanpour2؛ Reza Memarbashi2 | ||
| 1Department of Mathematics, Semnan University, Semnan, Iran | ||
| 2Department of Mathematics, Semnan University, Semnan, Iran. | ||
| تاریخ دریافت: 11 اردیبهشت 1397، تاریخ بازنگری: 23 خرداد 1397، تاریخ پذیرش: 27 فروردین 1398 | ||
| چکیده | ||
| The inverse problem considered in this paper is devoted to reconstruction of the unknown source term in parabolic equation from additional information which is given by measurements at final time. The cost functional is introduced and existence of the minimizer for this functional is established. The numerical algorithm to solve the inverse problem is based on the Ritz-Galerkin method with shifted Legendre polynomials as basis functions. Finally, some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for test example. | ||
| کلیدواژهها | ||
| Inverse source Problem؛ Cost Functional؛ Ill-Posed Problem؛ Regularization Method؛ Ritz-Galerkin Method | ||
| مراجع | ||
|
[1] O.M. Alifanov, Inverse Heat Transfer Problems, Springer Science & Business Media, 2012. [2] R. Askey, Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, 1975. [3] J. Bear, Dynamics of fluids in porous media, Elsevier, New York, 1972. [4] V. Beck and B. Blackwell, Inverse Heat Conduction, Ill-posed Problems, Wiley Interscience, New York, 1985. [5] J. Billingham, and B. Needham, The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves, Phil. Trans. R. Soc. Lond. A 334 (1991) 1–24. [6] J.R. Cannon, Determination of an unknown heat source from over-specified boundary data, SIAM J. Numer. Anal., 5(2) (1968), 275–286. [7] H.W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Springer Science & Business Media, 1996. [8] P.C. Hansen and D.P. O’Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput.14(6) (1993) 1487-1503. [9] P.C. Hansen, Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems, Numerical Algorithms 6(1) (1994) 1–35. [10] V. Isakov, Inverse problems for partial Differential Equations, Springer, New York, 1998. [11] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problem, Springer, New York, 1999. [12] J.D. Murray, Mathematical Biology, 3rd ed, Interdisciplinary Applied Mathematics vol 17, New York, Springer, 2002. [13] A. Shidfar, A. Babaei, and A. Molabahrami. Solving the inverse problem of identifying an unknown source term in a parabolic equation, Comput. Math. Appl. 60(5) (2010) 1209–1213. [14] A. Shidfar, G.R. Karamali, and J. Damirchi, An inverse heat conduction problem with a nonlinear source term, Nonlinear Anal.: Theory Meth. Appl. 65(3) (2006) 615–621. [15] A.N. Tikhonov, V.I. Arsenin, and F. John, Solutions of ill-posed, Washington, DC: Winston, 1977. [16] L. Yan, F.L. Yang, and C.L. Fu, A meshless method for solving an inverse space-wise-dependent heat source problem, J. Comput. Phys. 228(1) (2009) 123–136. [17] S.A. Yousefi, Z. Barikbin, and M. Dehghan, Ritz-Galerkin method with Bernstein polynomial basis for finding the product solution form of the heat equation with non-classic boundary conditions, Int. J. Numer. Meth. Heat Fluid Flow 22(1) (2012) 39–48. [18] Z. Yi and D.A. Murio, Source term identification in 1-D IHCP, Comput. Math. Appl. 74(12) (2004) 1921–1933. | ||
|
آمار تعداد مشاهده مقاله: 16,092 تعداد دریافت فایل اصل مقاله: 9,553 |
||