In this paper we construct a new set of basis functions for the numerical solution of nonhomogeneous heat conduction problems with Dirichlet boundary conditions and null initial data. These functions can be seen as Newtonian potentials of plane waves for the heat equation and satisfy a null initial condition. Density results for adapted waves will be established and several numerical simulations will be presented in order to discuss the accuracy and feasibility of the proposed method. An application of the method for heat problems with non null initial temperature will also be discussed.

中文翻译：

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一种适用于热传导问题的平面波方法

在本文中，我们为具有 Dirichlet 边界条件和零初始数据的非齐次热传导问题的数值解构造了一组新的基函数。这些函数可以看作是热方程的平面波的牛顿势，并且满足零初始条件。将建立适应波的密度结果，并提出几个数值模拟，以讨论所提出方法的准确性和可行性。还将讨论该方法在具有非零初始温度的热问题中的应用。