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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.

In this article, a nonic B-spline collocation approach is applied to solve the approximate solution of Kuramoto-Sivashinsky equation (KSE). Here the nonlinear term of KSE is linearizing using Taylor series technique. The main objective of this study is to provide a new class of approach by applying some possible higher-order derivatives rather than lower order derivatives of the nonic B-spline on the boundary conditions of KSE in finding the additional constraints, which help us to obtain a unique solution of the problem. The stability analysis is investigated using the Von-Neumann scheme and the proposed scheme is found to be unconditionally stable. The efficiency and accuracy of the proposed approach are demonstrated by two numerical tests and the current results are compared with the exact solution and result of others in the literature.

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