Numerical experiments on the accuracy of ENO and modified ENO schemes

In this paper we make further numerical experiments assessing an accuracy degeneracy phenomena reported by A. Rogerson and E. Meiburg (this issue, 1990). We also propose a modified ENO scheme, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives results comparable to the original ENO schemes for discontinuous problems.Research supported by NSF grant No. DMS88-10150, NASA Langley contract No. NAS1-18605, and AFOSR grant No. 90-0093. Computation supported by NAS.