Volume 2, Issue 2
Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems.

Igor Boglaev

Int. J. Numer. Anal. Mod. B,2 (2011), pp. 109-123

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  • Abstract

This paper deals with numerical solving semilinear parabolic problems based on the method of upper and lower solutions. A monotone iterative method with quadratic convergence rate is constructed. The monotone iterative method combines an explicit construction of initial upper and lower solutions and the modified accelerated monotone iterative method. The monotone iterative method leads to the existence-uniqueness theorem. An analysis of convergence rates of the monotone iterative method, based on different stoping tests, is given. Results of numerical experiments are presented, where iteration counts are compared with a monotone iterative method, whose convergence rate is linear.

  • History

Published online: 2011-02

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