This paper presents applications of boundary element method (BEM) in engineering to numerically analyse the Telegraph equation in two dimensions for two cases. For this purpose, the mathematical model developed is called D-BEM, uses a time independent fundamental solution and the Finite Difference Method is combined to BEM to approximate the derivative time terms and the Gauss Quadrature is used for calculation of domain integrals. The solution of the system of equations is based on the Gaussian elimination method, being verified the stability of the proposed formulation with a correlation level greater than 0.9, estimated from the dispersion coefficient R² between the analytical solution and the D-BEM solution. The D-BEM formulation was used to solve a variation of the Telegraph equation, called the Reaction-telegraph equation, in which the value of the delay parameter λ was varied, obtaining interesting results for the population density simulating the dynamics of population invasion, similar to the problem of tumour growth or cancer progression in four examples analysed. The numerical results of the Telegraph equation, as well as the entire formulation of the boundary elements are presented below.

本文介绍了边界元法（BEM）在工程中对二维电报方程进行二维数值分析的两种情况。为此，开发的数学模型称为D-BEM，它使用与时间无关的基本解，并将有限差分法与BEM结合起来以近似导数时间项，并且使用高斯求积法计算域积分。方程组的解基于高斯消去法，通过色散系数R ²估计，相关度大于0.9的拟议公式的稳定性得到了验证在分析解决方案和D-BEM解决方案之间。D-BEM公式用于解决电报方程的一个变种，称为反应电报方程，其中延迟参数λ的值发生变化，从而为模拟人口入侵动态的人口密度获得了有趣的结果，类似分析了四个例子中关于肿瘤生长或癌症进展的问题。电报方程的数值结果以及边界元素的完整公式如下所示。