A decatic B-spline collocation technique is employed to compute the numerical result of a nonlinear Burgers' equation. The nonlinear term of Burgers' equation is locally linearized using Taylor series technique. The present method is effective for the approximate solution of Burgers' with a very small value of kinematic viscosity “a.” Some illustrated numerical experiments are taken into consideration to focus on the importance of the current work and some comparative studies are reported with others as well as with the exact solutions. The linear stability of the method is analyzed with Von Neumann technique. Application of higher-order derivatives rather than lower-order derivatives of the decatic B-splines on the boundary conditions is the keynote to obtain a better approximate solution of the present method.

中文翻译：

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伯格斯方程近似解的德卡B样条配置方案

采用decatic B样条配置技术计算非线性Burgers方程的数值结果。Burgers 方程的非线性项使用泰勒级数技术进行局部线性化。本方法对于运动粘度“ a ”值很小的 Burgers 近似解是有效的” 考虑了一些有说明的数值实验，以关注当前工作的重要性，并报告了一些与其他研究以及精确解决方案的比较研究。用冯诺依曼技术分析了该方法的线性稳定性。在边界条件上应用decatic B样条的高阶导数而不是低阶导数是获得本方法更好近似解的关键。