The current paper concerns to develop a new meshless numerical procedure to solve heat transport equation. For this aim, the Crank–Nicolson finite difference idea is used to discrete the time derivative. Thus, a time-discrete scheme is derived. The unconditional stability and convergence of the time-discrete scheme are proved by energy method. Then, the interpolating element-free Galerkin method is applied to get a full-discrete scheme. Furthermore, the convergence rate of the full-discrete formulation is studied. At the end, some examples are considered to compare the theoretical results with the computational results and also to show the efficiency and ability of the proposed numerical procedure.

目前的论文涉及开发一种新的无网格数值程序来求解热传输方程。为此，使用 Crank-Nicolson 有限差分思想来离散时间导数。因此，推导出时间离散方案。用能量法证明了时间离散方案的无条件稳定性和收敛性。然后，应用插值无元Galerkin方法得到全离散方案。此外，研究了全离散公式的收敛速度。最后，考虑了一些例子，将理论结果与计算结果进行比较，并展示所提出的数值程序的效率和能力。