An unconventional approach is applied to solve the one-dimensional Burgers' equation. It is based on spline polynomial interpolations and Hopf-Cole transformation. Taylor expansion is used to approximate the exponential term in the transformation, then the analytical solution of the simplified equation is discretized to form a numerical scheme, involving various special functions. The derived scheme is explicit and adaptable for parallel computing. However, some types of boundary condition cannot be specified straightforwardly. Three test cases were employed to examine its accuracy, stability, and parallel scalability. In the aspect of accuracy, the schemes employed cubic and quintic spline interpolation performs equally well, managing to reduce the $\ell_{1}$, $\ell_{2}$ and $\ell_{\infty}$ error norms down to the order of $10^{-4}$. Due to the transformation, their stability condition $\nu \Delta t/\Delta x^2 > 0.02$ includes the viscosity/diffusion coefficient $\nu$. From the condition, the schemes can run at a large time step size $\Delta t$ even when grid spacing $\Delta x$ is small. These characteristics suggest that the method is more suitable for operational use than for research purposes.

翻译：采用一种非常规方法求解一维Burgers方程。该方法基于样条多项式插值和Hopf-Cole变换。利用泰勒展开逼近变换中的指数项，随后将简化方程的解析解离散化，形成包含多种特殊函数的数值格式。所推导的格式为显式格式，适用于并行计算，但无法直接指定某些类型的边界条件。通过三个测试案例检验了该方法的精度、稳定性和并行扩展性。在精度方面，采用三次与五次样条插值的格式表现同样出色，能将$\ell_{1}$、$\ell_{2}$和$\ell_{\infty}$误差模量降至$10^{-4}$量级。由于变换的存在，其稳定性条件$\nu \Delta t/\Delta x^2 > 0.02$包含了黏性/扩散系数$\nu$。根据该条件，即使网格间距$\Delta x$较小，格式也能采用较大的时间步长$\Delta t$运行。这些特性表明，该方法更适合实际应用而非研究目的。