This study carries the novel applications of the Sinc collocation method to investigate the numerical computing paradigm of Schrödinger wave equation and Transport equation as a great level of accuracy and precision. A global collocation-based Sinc function is embedded with a cardinal expansion to discretize initially time derivatives by finite difference method and secondly spatial derivatives are approximated with \(\theta \)-weighted scheme. Sinc collocation method (SCM) is found to be a more robust approach in order to avoid singularities in proposed problems and for yielding accurate numerical results. The governing PDEs are transformed with the help of Sinc function into algebraic system of equations, and further, these algebraic equations are solved with the help of computational iteration scheme to obtain the numerical results. The scheme provides a reliable and excellent procedure for adaptation of finding unknown in Sinc function for these problems. An extensive stability analysis is done to validate the convergence, accuracy and exactness of the proposed scheme.

本研究采用了 Sinc 搭配方法的新应用，以研究薛定谔波动方程和输运方程的数值计算范式，具有很高的准确度和精度。基于全局搭配的 Sinc 函数嵌入基数展开式以通过有限差分方法离散初始时间导数，其次空间导数近似为\(\theta \)-加权方案。Sinc 搭配方法 (SCM) 被发现是一种更稳健的方法，以避免提出的问题中的奇异性并产生准确的数值结果。利用Sinc函数将控制偏微分方程转化为代数方程组，并进一步借助计算迭代方案求解这些代数方程以获得数值结果。该方案为适应这些问题在 Sinc 函数中寻找未知数提供了一个可靠和优秀的过程。进行了广泛的稳定性分析，以验证所提出方案的收敛性、准确性和准确性。