Abstract
SummaryThis article presents an improved fifth‐order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton‐Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L1‐norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one‐ and two‐dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.
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