Volume 1, Issue 5
Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation

Dang Quang A and Le Tung Son

10.4208/aamm.09-m0925

Adv. Appl. Math. Mech., 1 (2009), pp. 683-698.

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  • Abstract

The solution of boundary value problems (BVP) for fourth order differential equations by their reduction to BVP for second order equations, with the aim to use the available efficient algorithms for the latter ones, attracts attention from many researchers. In this paper, using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic physics. The convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.

  • History

Published online: 2009-01

  • AMS Subject Headings

65N99, 65Z05, 76M25

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