In this article, we study the heat transfer problems which typically occur in nonlinear models. Since nonlinearity causes time-consuming and difficulty in finding analytical solutions, we focus on the Chebyshev wavelets method which is a powerful computational scheme for approximating solutions. In the proposed method, we apply the Chebyshev wavelets to expand the solution through the corresponding operational matrix of integration. Moreover, the efficiency of this approach is experimentally compared with the homotopy perturbation method, differential transformation method and variational iteration method which approves the efficiency of our method rather than the analytical methods in overcoming the nonlinearity.

在本文中，我们研究了非线性模型中通常出现的传热问题。由于非线性导致寻找解析解的耗时和困难，我们专注于切比雪夫小波方法，这是一种用于逼近解的强大计算方案。在所提出的方法中，我们应用切比雪夫小波通过相应的积分运算矩阵来扩展解。此外，该方法的效率与同伦微扰法、微分变换法和变分迭代法进行了实验比较，这证明了我们的方法而不是解析方法在克服非线性方面的效率。