  In the present work, we propose two new variants of fifth order finite
difference WENO schemes of adaptive order. We compare our proposed schemes with
other variants of WENO schemes with special emphasize on WENO-AO(5,3) scheme
[Balsara, Garain, and Shu, {\it J. Comput. Phys.}, 326 (2016), pp 780-804]. The
first algorithm (WENO-AON(5,3)), involves the construction of a new simple
smoothness indicator which reduces the computational cost of WENO-AO(5,3)
scheme. Numerical experiments show that accuracy of WENO-AON(5,3) scheme is
comparable to that of WENO-AO(5,3) scheme and resolution of solutions involving
shock or other discontinuities is comparable to that of WENO-AO(5,3) scheme.
The second algorithm denoted as WENO-AO(5,4,3), involves the inclusion of an
extra cubic polynomial reconstruction in the base WENO- AO(5,3) scheme, which
leads to a more accurate scheme. Extensive numerical experiments in 1D and 2D
are performed, which shows that WENO-AO(5,4,3) scheme has better resolution
near shocks or discontinuities among the considered WENO schemes with
negligible increase in computational cost.
