In this article, a meshfree spectral interpolation technique combined with Crank–Nicolson difference scheme is proposed to solve a class of strongly non-linear Burgers–Fisher type equation numerically. The proposed technique utilizes meshless shape functions for approximation of unknown spatial function and its derivatives. These shape functions are obtained by combining radial basis functions and point interpolation method in the spectral framework. The Crank–Nicolson finite difference scheme is employed for time integration. Stability of the proposed method is analysed theoretically and supported by numerical evidences for RBFs shape parameter $\left(c\right)$, which is an equally important task. Measure of fitness quality is assessed via $L_{\mathrm{\infty }}$, $L_2$ and $L_{\mathrm{r}\mathrm{m}\mathrm{s}}$ error norms. Efficiency and accuracy of the proposed technique is further examined via variation of time-step size $\delta t$ and number of nodal points N. Comparison made with existing techniques in the literature confirms excellent performance of the proposed scheme.

在本文中，提出了一种结合Crank-Nicolson差分格式的无网格谱插值技术来数值求解一类强非线性Burgers-Fisher型方程。所提出的技术利用无网格形状函数来逼近未知空间函数及其导数。这些形状函数是在谱框架中结合径向基函数和点插值法得到的。Crank-Nicolson 有限差分格式用于时间积分。从理论上分析了所提出方法的稳定性，并得到了 RBF 形状参数的数值证据的支持$\left(C\right)$，这是一项同样重要的任务。健身质量的衡量标准是通过${升}_{\mathrm{\infty }}$, ${升}_2$ 和 ${升}_{\mathrm{r}\mathrm{米}\mathrm{秒}}$错误规范。通过时间步长的变化进一步检查了所提出技术的效率和准确性$\delta 吨$和节点数N。与文献中现有技术的比较证实了所提出方案的优异性能。