Abstract
This chapter discusses a new sixth-order difference scheme, exploiting the Richardson extrapolation compact technique (REC) and an operator interpolation scheme to solve the convection diffusion equations. The sixth-order difference scheme is based on the fourth-order compact difference scheme and results in solving tridiagonal linear systems. A detailed derivation procedure for the one-dimensional (1D) problem and generalize it to the two dimensions through the alternating direction implicit (ADI) method is also provided. The REC scheme is explicit as only the approximate values of the solution function are computed. The combined compact difference (CCD) scheme is implicit as the approximate values of the first and second derivatives as well as the approximate values of the solution function are computed.
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