A collocation method with space–time radial polynomials for solving two–dimensional inverse heat conduction problems (IHCPs) is presented. The space–time radial polynomial series function is developed for spatial and temporal discretization of the government equation within the space–time domain. Because boundary and initial data are assigned on the space–time boundaries, the numerical solution of the IHCP can be approximated by solving the inverse boundary value problem in the space–time domain without using the time–marching scheme. The inner, source, and boundary points are uniformly distributed using the proposed outer source space–time collocation scheme. Since all partial derivatives up to order of the problem's operator of the proposed basis functions are a series of continuous functions, which are nonsingular and smooth, the numerical solutions are obtained without using the shape parameter. Numerical examples for solving IHCPs with missing both parts of initial and boundary data are carried out. The results of our study are then compared with those of other collocation methods using multiquadric basis function. Results illustrate that highly accurate recovered temperatures are acquired. Additionally, the recovered temperatures on inaccessible boundaries with high accuracy can be acquired even 1/5 portion of the entire space–time boundaries are inaccessible.

提出了一种采用时空径向多项式的并置方法来求解二维逆导热问题（IHCP）。时空径向多项式级数函数是为时空域内政府方程的时空离散而开发的。由于边界和初始数据是在时空边界上分配的，因此可以通过解决时空域中的逆边界值问题而无需使用时间步进方案来近似计算IHCP的数值解。内部，源和边界点使用建议的外部源时空搭配方案均匀分布。由于所提出的基本函数中直至问题运算符阶数的所有偏导数都是一系列连续函数，它们是非奇异且平滑的，无需使用shape参数即可获得数值解。进行了求解缺少初始数据和边界数据的IHCP的数值示例。然后将我们的研究结果与使用多二次基函数的其他搭配方法进行比较。结果表明获得了高精度的恢复温度。此外，即使无法访问整个时空边界的1/5部分，也可以高精度获取在难以接近的边界上恢复的温度。结果表明获得了高精度的恢复温度。此外，即使无法访问整个时空边界的1/5部分，也可以高精度获取在难以接近的边界上恢复的温度。结果表明获得了高精度的恢复温度。此外，即使无法访问整个时空边界的1/5部分，也可以高精度获取在难以接近的边界上恢复的温度。