Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Abstract
In this paper a nonlinear backward parabolic problem in one dimensional space is considered. Using a suitable iterative algorithm, the problem is converted to a linear backward parabolic problem. For the corresponding problem, the backward finite differences method with suitable grid size is applied. It is shown that if the coefficients satisfy some special conditions, this algorithm not only is convergent, but also is conditionally stable. Moreover, it is proved that the estimated values converge to the exact solution of the problem. Al these approaches examined in some numerical examples. corresponding theorems for the convergency and stability of the solution are studied.
Zakeri, A., Jannati, Q., & Amiri, A. (2015). A numerical scheme for solving nonlinear backward parabolic problems. Bulletin of the Iranian Mathematical Society, 41(6), 1453-1464.
MLA
A. Zakeri; Q. Jannati; A. Amiri. "A numerical scheme for solving nonlinear backward parabolic problems". Bulletin of the Iranian Mathematical Society, 41, 6, 2015, 1453-1464.
HARVARD
Zakeri, A., Jannati, Q., Amiri, A. (2015). 'A numerical scheme for solving nonlinear backward parabolic problems', Bulletin of the Iranian Mathematical Society, 41(6), pp. 1453-1464.
VANCOUVER
Zakeri, A., Jannati, Q., Amiri, A. A numerical scheme for solving nonlinear backward parabolic problems. Bulletin of the Iranian Mathematical Society, 2015; 41(6): 1453-1464.
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