Development and analysis of exponential compact higher order schemes

Finite difference methods are more suitable for the complex mathematical models, because of its simplicity. Especially, for the high Reynolds number flows and turbulence models, the exponential higher order compact methods are more suitable due to several reasons discussed here, one of them is the method is highly efficient to resolve the dissipation and dispersion error components. This work contains a class of higher order methods and provide new error analysis techniques using discrete Fourier transformations. These class of higher order methods are suitable for both steady and unsteady model problems and uniformly high accurate for convection dominated case.