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首页> 外文期刊>Numerical analysis and applications >Peculiarities of Error Accumulation in Solving Problems for Simple Equations of Mathematical Physics by Finite Difference Methods
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Peculiarities of Error Accumulation in Solving Problems for Simple Equations of Mathematical Physics by Finite Difference Methods

机译：用有限差分法求解简单的数学物理方程式问题中累积误差的特殊性

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摘要

A mixed problem for the one-dimensional heat conduction equation with several versions of initial and boundary conditions is considered. To solve this problem, explicit and implicit schemes are used. Sweep and iterative methods are used for the implicit scheme when solving the system of equations. Numerical filtering of a finite sequence of results obtained for various grids with an increasing number of node points is used to analyze the method and rounding errors. To investigate rounding errors, the results obtained for various machine word mantissa lengths are compared. The numerical solution of a mixed problem for the wave equation is studied by similar methods. Some deterministic dependencies of the numerical method and rounding errors on the spatial coordinates, time, and the number of nodes are found. Some models of sources to describe the behavior of the errors in time are constructed. They are based on the results of computational experiments under various conditions. According to these models, which have been experimentally verified, the errors increase, decrease, or stabilize in time under the conditions, similarly to energy or mass.
机译：考虑具有初始和边界条件的几种形式的一维热传导方程的混合问题。为了解决这个问题，使用了显式和隐式方案。求解方程组时，隐式方案使用扫掠和迭代方法。对节点数目不断增加的各种网格获得的有限结果序列进行数值滤波，以分析该方法和舍入误差。为了研究舍入误差，比较了各种机器字尾数长度获得的结果。用相似的方法研究了波动方程混合问题的数值解。发现了数值方法的一些确定性依赖性以及在空间坐标，时间和节点数上的舍入误差。构建了一些描述时间错误行为的信息源模型。它们基于各种条件下的计算实验结果。根据已通过实验验证的这些模型，在类似于能量或质量的条件下，误差随时间的推移会增加，减少或稳定。

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