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Local solution method for numerical solving of the wave propagation problem

机译：数值求解波传播问题的局部解法

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摘要

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which s aimed at better representation of solutions in the regions of their rapid oscillations or exponential increase (decrease) is proposed. It is based on the approximation of the solution sought for in the form of a superposition of certain polynomial-exponential basic functions. The method is studied for the Helmholtz equation in comparison with the standard finite difference and finite element methods. The numerical tests have shown the convergence of the method proposed. In comparison with the standard methods the same accuracy is obtained on substantially coarser mesh. This advantage becomes more pronounced, if the solution varies very rapidly.
机译：提出了一种求解系数缓慢变化的常微分方程边界问题数值解的新方法，旨在更好地表示其快速振动或指数增加（减小）区域中的解。它基于某些多项式-指数基本函数的叠加形式所寻求的解决方案的近似值。与标准有限差分法和有限元法相比，研究了Helmholtz方程的方法。数值试验表明了该方法的收敛性。与标准方法相比，在实质上较粗的网格上可获得相同的精度。如果解决方案变化非常快，则此优势将变得更加明显。

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