Mathematical modeling of diffusion problem

Salemi, Maryam; Attary, Maryam

doi:10.22075/ijnaa.2019.18118.1989

Mathematical modeling of diffusion problem

Document Type : Research Paper

Authors

Maryam salemi

Maryam Attary

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

10.22075/ijnaa.2019.18118.1989

Abstract

‎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.

Keywords

‎Integral-algebraic equations‎

‎Diffusion model‎

‎Singular systems‎

Numerical treatment

[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.