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A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation

机译：求解二维线性双曲电报方程的无网格技术的比较研究

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摘要

In this paper, a comparison between two common techniques based on the radial basis function (RBFs), direct and indirect approaches and their localized forms is performed to numerical investigation of the two-dimensional linear second-order hyperbolic telegraph equation. Four meshfree methods based on the strong form equation, the nonsymmetric radial basis function collocation method or Kansa's method, the method of approximate particular solutions and the localized versions of these methods are formulated and the performances of these methods for solving governing problem are compared. A time stepping approach is employed for the first and second order time derivatives. The multiquadrics (MQ) and inverse multiquadrics (IMQ) functions are used as basis functions for interpolating either unknown function or Laplacian of the unknown function in the proposed techniques. Some numerical results are given to demonstrate the validity and efficiency of these methods. Through the presented results, it can be observed that local versions of the methods have superior stability and efficiency and the global methods are sensitive to the shape parameter and large amount of collocation points.
机译：本文对两种基于径向基函数（RBF）的常用技术，直接方法和间接方法及其局部形式进行了比较，以对二维线性二阶双曲线电报方程进行数值研究。根据强形式方程，非对称径向基函数配置法或Kansa方法，近似特殊解法和这些方法的局部形式，提出了四种无网格方法，并比较了这些方法解决控制问题的性能。一阶和二阶时间导数采用时间步进方法。在所提出的技术中，将多二次方（MQ）和逆多二次方（IMQ）函数用作内插未知函数或未知函数的拉普拉斯算子的基础函数。数值结果表明了这些方法的有效性和有效性。通过给出的结果，可以观察到该方法的局部版本具有优异的稳定性和效率，并且全局方法对形状参数和大量的并置点敏感。

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