Spectral resolutioned exponential compact higher order scheme (SRECHOS) for convection–diffusion equations

A spectral resolutioned exponential compact higher order scheme (SRECHOS) is developed to solve stationary convection–diffusion type of differential equations with constant convection and diffusion coefficients. The scheme is O(h6)O(h6) for one-dimensional problems and produces a tri-diagonal system of equations that can be solved efficiently using Thomas algorithm. For two-dimensional problems, the scheme produces an O(h4+k4)O(h4+k4) accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit (ADI) procedure. The efficiency of the developed scheme is measured using wave number analysis. The analysis shows that the SRECHOS has a much better spectral resolution than any of the existing higher order schemes. Numerical examples are solved and better performance of the SRECHOS in terms of accuracy over the existing schemes in the literature is demonstrated.