In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving computational efficiency. Both mixed and Robin-type boundary conditions are treated. In contrast with alternative, related methodologies, stability and convergence are unconditional. In particular, we prove unconditional, energy stability and optimal-order error estimates. A battery of numerical tests are presented to illustrate both the theory and application of these algorithms.

翻译：在本文中,我们提出了以不确定的温度依赖热传导性解决热方程式的第一阶精确数字方法。每种算法都为组合组合组合制的提高计算效率提供了共同系数矩阵。混合和罗宾型边界条件都得到了处理。与替代办法相反,相关方法、稳定性和趋同是无条件的。特别是,我们证明无条件、能源稳定性和最佳顺序误差估计。提供了一组数字测试,以说明这些算法的理论和应用。