In the present manuscript, approximate solution for 1D heat conduction equation will be sought with the Septic Hermite Collocation Method (SHCM). To achieve this goal, by means of the roots of both Chebyschev and Legendre polinomials used at the inner collocation points, the pseudo code of this method is found out and applied using Matlab, one of the widely used symbolic programming platforms. Furthermore, to illustrate the accuracy and effectiveness of this newly presented scheme, a comparison among analytical and numerical values is investigated. It has been illustrated that this scheme is both accurate and effective one and at the same time can be utilized in a successful way for finding out numerical solutions of several problems both linear and nonlinear.

翻译：本文旨在利用七次Hermite配置法（SHCM）求解一维热传导方程的近似解。为实现该目标，通过采用Chebyshev多项式和Legendre多项式的根作为内部配置点，推导出该方法的伪代码，并利用广泛使用的符号编程平台Matlab进行实现。此外，为验证所提新方法的准确性和有效性，对解析解与数值解进行了对比分析。结果表明，该方案既精确又有效，同时可成功应用于求解线性和非线性问题的数值解。