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

Quang A Dang & Le Tung Son

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

Published online: 2009-01

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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.

  • Keywords

Iterative method, biharmonic equation, mixed boundary conditions.

  • AMS Subject Headings

65N99, 65Z05, 76M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-683, author = {Quang A and Dang and and 20563 and and Quang A Dang and Le Tung and Son and and 20564 and and Le Tung Son}, title = {Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {5}, pages = {683--698}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0925}, url = {http://global-sci.org/intro/article_detail/aamm/8391.html} }
TY - JOUR T1 - Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation AU - Dang , Quang A AU - Son , Le Tung JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 683 EP - 698 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m0925 UR - https://global-sci.org/intro/article_detail/aamm/8391.html KW - Iterative method, biharmonic equation, mixed boundary conditions. AB -

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.

Dang Quang A & Le Tung Son. (1970). Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation. Advances in Applied Mathematics and Mechanics. 1 (5). 683-698. doi:10.4208/aamm.09-m0925
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