In this work, numerical solution of nonlinear modified Burgers equation is obtained using an improvised collocation technique with cubic B‐spline as basis functions. In this technique, cubic B‐splines are forced to satisfy the interpolatory condition along with some specific end conditions. Crank–Nicolson scheme is used for temporal domain and improvised cubic B‐spline collocation method is used for spatial domain discretization. Quasilinearization process is followed to tackle the nonlinear term in the equation. Convergence of the technique is established to be of order O(h⁴ + Δt²). Stability of the technique is examined using von‐Neumann analysis. L₂ and L_∞ error norms are calculated and are compared with those available in existing works. Results are found to be better and the technique is computationally efficient, which is shown by calculating CPU time.

中文翻译：

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求解特定Burgers方程的具有特定最终条件的简易搭配算法

在这项工作中，使用改进的搭配技术，以三次B样条作为基函数，获得了非线性修正Burgers方程的数值解。在这种技术中，三次B样条被强制满足插值条件以及某些特定的结束条件。Crank–Nicolson方案用于时域，而改进的三次B样条搭配方法用于空间域离散化。遵循拟线性化过程来解决方程中的非线性项。确定该技术的收敛性为O（h ⁴  + Δt ²）阶。使用von-Neumann分析检查技术的稳定性。L ₂和L计算_∞误差范数，并将其与现有工作中可用的范数进行比较。发现结果更好，并且该技术具有计算效率，这可以通过计算CPU时间来显示。