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Dang Quang A.; Nguyen Van Thien

Iterative method for solving the second boundary value problem for biharmonic-type equation. (English) Zbl 1251.65105

J. Appl. Math. 2012, Article ID 891519, 18 p. (2012).
Summary: 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.

Cited in 2 Documents

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Keywords:

fourth-order differential equations; second boundary value problem; biharmonic-type equation
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\textit{Dang Quang A} and \textit{Nguyen Van Thien}, J. Appl. Math. 2012, Article ID 891519, 18 p. (2012; Zbl 1251.65105)
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