In this article, we introduce a new method for increasing the accuracy of the fifth-order WENO scheme. Recently, some methods were developed to increase the accuracy near discontinuities. We use the idea of these methods and the mapped WENO schemes to increase the accuracy both in smooth regions and near discontinuities. We also present some numerical experiments including the linear wave equation and Euler equations of gas dynamics to confirm the theoretical results. The results show that the introduced scheme attains better resolution at the smooth parts of the solution, while keeping the same non-oscillatory behavior of the WENO schemes at shocks and discontinuities.
Mahmoodi Darian, H. (2025). A new method for increasing the accuracy of the fifth-order WENO scheme. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.65032.2973
MLA
Mahmoodi Darian, H. . "A new method for increasing the accuracy of the fifth-order WENO scheme", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.65032.2973
HARVARD
Mahmoodi Darian, H. (2025). 'A new method for increasing the accuracy of the fifth-order WENO scheme', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.65032.2973
CHICAGO
H. Mahmoodi Darian, "A new method for increasing the accuracy of the fifth-order WENO scheme," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.65032.2973
VANCOUVER
Mahmoodi Darian, H. A new method for increasing the accuracy of the fifth-order WENO scheme. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.65032.2973
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