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Mathematical modeling of diffusion problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 171، دوره 13، شماره 1، خرداد 2022، صفحه 2065-2073 اصل مقاله (462.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.18118.1989 | ||
| نویسندگان | ||
| Maryam salemi؛ Maryam Attary* | ||
| Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran | ||
| تاریخ دریافت: 03 تیر 1398، تاریخ پذیرش: 12 شهریور 1398 | ||
| چکیده | ||
| This work aims to introduce a numerical approximation procedure based on an operational matrix of block pulse functions, which is employed in solving integral-algebraic equations arising from the diffusion model. It is known that the integral-algebraic equations belong to the class of singular problems. The main advantage of this method is the reduction of these singular systems by using an operational matrix to linear lower triangular systems of algebraic equations, which is non-singular. An estimation of the error and illustrative instances are discussed to evaluate the validity and applicability of the presented method. | ||
| کلیدواژهها | ||
| Integral-algebraic equations؛ Diffusion model؛ Singular systems؛ Numerical treatment | ||
| مراجع | ||
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[1] M.V. Bulatov and V.F. Chistyakov, The properties of differential-algebraic systems and their integral analogues, Memorial University of Newfoundland, Preprint, 1997. [2] J.P. Kauthen, The numerical solution of integral-algebraic equations of index-1 by polynomial spline collocation methods, Math. Comp. 236 (2000) 1503—1514. [3] M. Hadizadeh, F. Ghoreishi and S. Pishbin, Jacobi spectral solution for integral algebraic equations of index-2, Appl. Numer. Math. 61 (2011) 131-–148. [4] K. Maleknejad, H. Safdari and M. Nouri, Numerical solution of an integral equations system of the first kind by using an operational matrix with block pulse functions, Int. J. Syst. Sci. 42 (2011). [5] H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, University Press, Cambridge, 2004. [6] A.I. Zenchuk, Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation, J. Nonlinear Math. Phys. 15 (2008) 437-448. [7] J.R. Cannon, The One-Dimensional Heat Equation, University Press, Cambridge, 1984. [8] C.W. Gear, Differential-algebraic equations, indices, and integral-algebraic equations, SIAM. J. Numer. Anal. 27 (1990) 1527—1534. | ||
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