Abstract A gradually implicit method with deferred correction (GIMDC) and adaptive relaxation factors (ARFs) is developed for simulation to nonlinear heat transfer with temperature-dependent properties. GIMDC is equivalent to explicit method initially and approaches implicit method gradually. The theoretical analyses of convergence, error and stability indicate that the accuracy and stability of GIMDC are close to implicit method if ARFs are utilized to guarantee convergence. A strict condition for ARFs is derived. GIMDC is compared with PEM (pure explicit method), NIM (Newton iterative method for implicit solution) and FEM (finite element method) which shows that GIMDC is of acceptable numerical accuracy (similar to NIM and 19.28% and 12.89% higher than PEM and FEM respectively in average) and higher efficiency. The numerical tests are presented which shows that using optimized ARFs (confined by strict condition), efficiency, accuracy and stability are ensured.

中文翻译：

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一种具有延迟校正和自适应松弛因子的渐隐式非线性传热模拟方法

摘要 为了模拟具有温度相关特性的非线性传热，开发了一种具有延迟校正（GIMDC）和自适应松弛因子（ARF）的渐隐式方法。GIMDC最初等价于显式方法，逐渐接近隐式方法。收敛性、误差和稳定性的理论分析表明，如果利用ARFs来保证收敛性，GIMDC的精度和稳定性接近于隐式方法。导出了 ARF 的严格条件。GIMDC 与 PEM（纯显式方法）、NIM（隐式求解的牛顿迭代法）和 FEM（有限元方法）进行比较，表明 GIMDC 具有可接受的数值精度（与 NIM 相似，比 PEM 和 PEM 分别高 19.28% 和 12.89%）。 FEM 分别平均）和更高的效率。