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A Radial Basis Function Collocation Method for Space-dependent Inverse Heat Problems | ||
| Journal of Applied and Computational Mechanics | ||
| مقاله 13، دوره 6، Special Issue، اسفند 2020، صفحه 1187-1199 اصل مقاله (1.91 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22055/jacm.2020.32999.2123 | ||
| نویسندگان | ||
| Muhammad Nawaz Khan1؛ Imtiaz Ahmad2؛ Hijaz Ahmad* 1 | ||
| 1Department of Basic Sciences, University of Engineering and Technology Peshawar 25000, Pakistan | ||
| 2Department of Mathematics, University of Swabi 23430, Khyber Pakhtunkhwa, Pakistan | ||
| چکیده | ||
| In this study, a radial basis function collocation method (RBFCM) is proposed for the numerical treatment of inverse space-wise dependent heat source problems. Multiquadric radial basis function is applied for spatial discretization whereas for temporal discretization Runge-Kutta method of order four is employed. Numerical experiments for one, two and three-dimensional cases are included to test the efficiency and accuracy of the suggested method. Both non-rectangular and rectangular geometries with uniform and non-uniform points are taken into consideration and the obtained results are compared with the exact as well as with the techniques presented in recent literature. | ||
| کلیدواژهها | ||
| Meshless method؛ Radial basis function؛ Inverse heat source problem؛ Non-uniform nodes؛ Non-rectangular domains | ||
| مراجع | ||
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[3] Srivastava MH, Ahmad H, Ahmad I, Thounthong P, Khan NM., Numerical simulation of three-dimensional fractional-order convection-diffusion PDEs by a local meshless method, Thermal Science, 2020, DOI: 10.2298/TSCI200225210S.
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[7] Wei T., Wang J., Simultaneous determination for a space-dependent heat source and the initial data by the MFS, Engineering Analysis with Boundary Elements 36 (12) (2012) 1848-1855.
[8] Ahmadabadi M. N., Ameri M. A., Ghaini F. M., The method of fundamental solutions for the inverse space-dependent heat source problem, Engineering Analysis with Boundary Elements 33 (10) (2009) 1231-1235.
[9] Liu C.-S., An iterative algorithm for identifying heat source by using a DQ and a Lie-group method, Inverse Problems in Science and Engineering 23 (1) (2015) 67-92.
[10] Siraj-ul-Islam, Ismail S., Meshless collocation procedures for time-dependent inverse heat problems, International Journal of Heat and Mass Transfer 113 (2017) 1152-1167.
[11] Niasar M. B., Ameri M. A., Moving mesh non-standard finite difference method for non-linear heat transfer in a thin finite rod, Journal of Applied and Computational Mechanics 4 (3) (2018) 161-166.
[12] Ahmad, H., Khan, T. A., Yao, S.-W., Numerical solution of second order Painlevé differential equation, Journal of Mathematics and Computer Science 21(2) (2020) 150-157.
[13] Flegg J. A., Byrne H. M., Flegg M. B., McElwain D. S., Wound healing angiogenesis: the clinical implications of a simple mathematical model, Journal of Theoretical Biology 300 (2012) 309-316.
[14] Ahmad, H., Khan, T. A., Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems, Noise & Vibration Worldwide 51 (2020) 12–20.
[15] Ahmad, H., Seadawy, A. R., Khan, T. A., Thounthong, P., Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations, Journal of Taibah University for Science 14 (2020) 346–358.
[16] Ahmad, H., Seadawy, A. R., Khan, T. A., Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm, Mathematics and Computers in Simulation (2020) doi: 10.1016/j.matcom.2020.04.005.
[17] Ahmad, H., Seadawy, A. R., Khan, T. A., Thounthong, P., Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations, Journal of Taibah University for Science 14 (2020) 346–358.
[18] Ghazanfari, S. A., Wahid, M. A., Heat transfer enhancement and pressure drop for fin-and-tube compact heat exchangers with delta winglet-type vortex generators, Facta Universitatis, Series: Mechanical Engineering 16 (2) (2018) 233-247.
[19] Ahmad, H., Khan, T. A., Durur, H., Ismail, G. M. & Yokus, A., Analytic approximate solutions of diffusion equations arising in oil pollution, Journal of Ocean Engineering and Science, 2020, doi: https://doi.org/10.1016/j.joes.2020.05.002.
[20] Ahmad, H., Khan, T. A. & Yao, S. W., An efficient approach for the numerical solution of fifth-order KdV equations, Open Mathematics, 18, 2020, 738–748.
[21] Siraj-ul-Islam, Ahmad I., A comparative analysis of local meshless formulation for multi- asset option models, Engineering Analysis with Boundary Elements 65 (2016) 159-176.
[22] Ahmad I, Ahmad H, Thounthong P, Chu YM, Cesarano C. Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method, Symmetry, 12(7), 2020, 1195.
[23] Ahmad I., Ahsan M., Zaheer-ud-Din, Ahmad M., Kumam P., An efficient local formulation for time-dependent PDEs, Mathematics 7 (2019) 216. | ||
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