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本文介绍了在与时间有关的或与时间无关的边界条件下解瞬时热传导问题的特征值法。这个空间域被分成一些有限元。并在每个有限元交点上得到作为时间函数的温度的闭式表达式。为了验证这种特征值法的优点，求解了有精确解的３个试验问题。甚至对于大网格来说，这种方法也能得到精确的结果。它在时间域中能提供精确的解，因此，这种方法不受一般数值技术的时间步的限制，根据初始条件可得到在任一给定时间的温度场，并且，无时间推进是必要条件。对于稳态解已知的一些问题，仅几个主特征值和它相应的特征矢量是需要计算的，这些特点可节省很多的计算时间，特别是对于持续时间较长的一些问题。此外，温度场闭式表达式的可用性使该方法对于一些耦合问题，例如固体－流体和热结构的相互作用，很有吸引力。
In this paper, we introduce the eigenvalue method for solving transient heat conduction problems under time-independent or time-independent boundary conditions. This space domain is divided into some finite elements. The closed-form expression of temperature as a function of time is obtained at each intersection of finite elements. In order to verify the advantages of this eigenvalue method, three experimental problems with exact solutions were solved. Even for large grid, this method can get accurate results. It provides an exact solution in the time domain. Therefore, this method is not limited by the time steps of the general numerical technique. The temperature field at any given time can be obtained from the initial conditions, and no time advance is necessary. For some of the known problems of steady-state solutions, only a few of the main eigenvalues and their corresponding eigenvectors need to be calculated. These features can save a lot of computational time, especially for longer duration problems. In addition, the usability of the closed form of the temperature field makes the method attractive for coupling problems such as solid-fluid interactions with thermal structures.