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

机译:解双调和型方程第二边值问题的迭代方法

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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.
机译:通过将四阶微分方程的边值问题简化为二阶微分方程的边值问题来解决其边值问题,其目的是将后者的应用成果加以利用,引起了许多研究者的关注。在本文中,我们利用自己在最近的工作中开发的技术,为双调和型方程构造了第二个BVP的迭代方法,该方法描述了双参数弹性地基上的板的挠度。确定了该方法的收敛速度。找到迭代参数的最佳值。几个数值例子证实了该方法的有效性。

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