FOUR NUMERICAL SCHEMES FOR SOLUTION OF BURGERS' EQUATION VIA OPERATOR SPLITTING TRIGONOMETRIC CUBIC B-SPLINE COLLOCATION METHOD

OpenAlex İngilizce

In this study, we have used operator splitting methods for numerical solutions of the Burgers' equation by given four different numerical schemes. To set these schemes, we divide the Burgers equation into two sub-problems according to the time term, as linear $ U_{t}=\mathcal{L}(U) $ and nonlinear $ U_{t}=\mathcal{N}(U) $. Then, numerical schemes have been obtained by the finite element method using trigonometric cubic B-spline basis for each sub-problem. Splitting $ \mathcal{L}\circ\mathcal{N} $, $ \mathcal{N}\circ\mathcal{L} $ Lie-Trotter and $ \mathcal{L}\circ\mathcal{N} \circ \mathcal{L} $, $ \mathcal{N\circ L\circ N} $ Strang splitting solution schemes have been used to obtain the solution of the main equation. Numerical results calculated with these schemes have been compared among themselves in terms of $ L_{2} $, $ L_{\infty} $ error norms and CPU time. Furthermore, the numerical results have been compared with some studies that solved the equation directly with the same method. It has been observed that the numerical results obtained with the proposed schemes are in agreement with the exact solution and other studies in the literature. All calculations are obtained using Matlab Version R2015a.