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Iterative Method for Solving the Second Boundary Value Problem for Biharmonic‐Type Equation

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  • Dang Quang A.
  • Nguyen Van Thien

Abstract

Solving boundary value problems (BVPs) for the fourth‐order differential equations by the reduction of them to BVPs for the second‐order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic‐type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.

Suggested Citation

  • Dang Quang A. & Nguyen Van Thien, 2012. "Iterative Method for Solving the Second Boundary Value Problem for Biharmonic‐Type Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:891519
    DOI: 10.1155/2012/891519
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    References listed on IDEAS

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    1. Aleksandr A. Samarskii & Evgenii S. Nikolaev, 1989. "Numerical Methods for Grid Equations," Springer Books, Springer, number 978-3-0348-9142-4, October.
    2. Aleksandr A. Samarskii & Evgenii S. Nikolaev, 1989. "Numerical Methods for Grid Equations," Springer Books, Springer, number 978-3-0348-9272-8, October.
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