On the use of the discrete analogue of the Rellich identity for the discrete 1D wave equation with Dirichlet boundary conditions

CUER M.

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On the use of the discrete analogue of the Rellich identity for the discrete 1D wave equation with Dirichlet boundary conditions

机译：在具有Dirichlet边界条件的离散一维波动方程中使用Rellich恒等式的离散模拟

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We observe that a finite differences analogue of the Rellich identity can be used to take into account the errors in the discretization of boundary conditions of 1D second order elliptic problems if the mesh points fall at ±h/2 but not at the boundary, h being the mesh size. It is shown that, in the case of the discrete 1D wave equation, there is an extra term in the analogue of the Rellich identity that does not allow to obtain a discrete version of the results of [1], [2]. But the numerical experiment shows that, with the usual schemes, there is no order reduction.

机译：我们观察到，如果网格点落在±h / 2而不是边界处，则可以使用Rellich等式的有限差分类似物来考虑一维二阶椭圆问题边界条件离散化中的误差。网格尺寸。结果表明，在离散一维波动方程的情况下，在Rellich恒等式中有一个额外的项，它不允许获得[1]，[2]结果的离散形式。但是数值实验表明，在通常的方案下，没有降阶。

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |1996年第s2期|p.503-504|共2页
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CUER M.;
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正文语种 eng
中图分类应用数学;
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1. ON THE USE OF THE DISCRETE ANALOGUE OF THE RELLICH IDENTITY FOR THE DISCRETE 1D WAVE EQUATION WITH DIRICHLET BOUNDARY CONDITIONS [J] . Cuer M. Zeitschrift fur Angewandte Mathematik und Mechanik . 1996,第s2期

机译：关于狄利克雷边界条件的离散一维波方程的Rellich身份的离散类比的使用
2. A class of quasi-variable mesh methods based on off-step discretization for the solution of non-linear fourth order ordinary differential equations with Dirichlet and Neumann boundary conditions [J] . Ranjan K Mohanty, Md Hasan Sarwer, Nikita Setia Advances in Difference Equations . 2016,第1期

机译：一类基于失步离散的拟变量网格方法，用于求解带狄利克雷和诺伊曼边界条件的非线性四阶常微分方程
3. The impact of the Dirichlet boundary conditions on the convergence of the discretized system of nonlinear equations for potential problems [J] . Jan Kucwaj Computer Assisted Mechanics and Engineering Sciences . 2016,第1期

机译：Dirichlet边界条件对离散非线性方程组收敛性的影响
4. SUFFICIENT OPTIMALITY CONDITIONS FOR DIRICHLET BOUNDARY CONTROL OF WAVE EQUATIONS [C] . Andrzej Nowakowski IEEE Conference on Decision and Control . 2008

机译：波动方程的Dirichlet边界控制的足够的最佳状态
5. Numerical methods for nonlinear partial differential equations of Gross-Pitaevskii type and their discrete analogues. [D] . Savytska, Nataliya Y. 2002

机译：Gross-Pitaevskii型非线性偏微分方程及其离散类似物的数值方法。
6. Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations [O] . Simeng Li, Nianbei Li -1

机译：一维类FPU离散非线性Schrödinger方程中的重新归一化振动和正常能量传输
7. A class of quasi-variable mesh methods based on off-step discretization for the solution of non-linear fourth order ordinary differential equations with Dirichlet and Neumann boundary conditions [O] . Ranjan K Mohanty, Md Hasan Sarwer, Nikita Setia 2016

机译：一类基于失步离散的拟变量网格方法，用于求解带狄利克雷和诺伊曼边界条件的非线性四阶常微分方程

On the use of the discrete analogue of the Rellich identity for the discrete 1D wave equation with Dirichlet boundary conditions

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