A modifying coefficient scheme based on essentially non-oscillatory scheme

Based on the widely used second-order essentially non-oscillatory(ENO) scheme, a modifying coefficient approach was defined on non-uniform mesh. By modifying its coefficient, without extending modifying coefficient ENO scheme's stencil, a new scheme was obtained. The new scheme gives the accuracy of one higher order, and preserves most of the properties (Upwind, TVD and TVD etc) of the primitive ENO scheme. The numerical experiments show that modifying coefficient ENO scheme is more efficient and of higher accuracy in smooth regions when compared with ENO scheme.