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Two-step deferred correction algorithm for the problem of fluid film squeezed between rotating disks

机译:转盘之间的液膜挤压问题的两步递延校正算法

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In this paper, a new collocation method is analyzed for the solution of a system of nonlinear differential equations arisen from modeling the flow of a Newtonian magnetic lubricant film with magnetic induction effects, squeezed between two rotating disks with a time-dependent distance. The source problem is a system of nonlinear partial differential equations which is converted to the system of fourth-order ordinary differential equations by some appropriate transformations. The problem is then transformed to an equivalent second-order system subject to its proper boundary conditions. Eighth-order superconvergent approximations are obtained for the solution based on sextic B-spline. High-order perturbations of the problem are used to find higher orders of convergence. We proceed the superconvergence in two successive steps by perturbing the right-hand side of the problem appropriately. The convergence of the method is analyzed via Green's function approach. The numerical results verify the theoretical orders of convergence and show the efficiency of the methods as well.
机译:在本文中,分析了一种新的搭配方法,用于求解非线性微分方程组的求解,该系统是通过对具有磁感应效应的牛顿磁性润滑膜的流动进行建模而产生的,该流动被挤压在两个随时间变化的转盘之间。源问题是非线性偏微分方程组,通过一些适当的变换将其转换为四阶常微分方程组。然后,根据问题的适当边界条件,将问题转换为等效的二阶系统。对于基于六边形B样条的解,获得了八阶超收敛近似。问题的高阶扰动可用于寻找更高阶的收敛性。我们通过适当扰动问题的右侧,在两个连续的步骤中进行超收敛。通过格林函数方法分析了该方法的收敛性。数值结果验证了理论上的收敛性,并证明了该方法的有效性。

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