ports at the molecular level. These two terms are treated separately and then combined to form the resulting discret-Conventional exponential difference schemes may yield accurate and stable solutions for the one-dimensional, source-free convec-ized expression in the conventional finite difference formution-diffusion equation. However, its accuracy will be deteriorated lation. For the diffusion term, the central difference scheme in the presence of a nonconstant source term or in multidimensional (CD) can provide an accurate and stable discretized repreproblems. Attempts are made to increase the accuracy of exponensentation. This central difference expression has a compact tial difference schemes. First, we propose an exponential difference three-point supported stencil in one dimension and yields scheme that retains second-order accuracy in the presence of a source term or in multidimensional situations. Mathematical analy-second-order accuracy in space. The resulting matrix equasis and numerical experiments are performed to validate this tion is diagonally dominant and can be solved by simple scheme. Second, a local particular solution method is introduced iterative methods. With this diagonal dominance property, to raise the solution accuracy for problems with a source term. This bounded solutions can be easily achieved. Similar central method locally transforms the original problem to a source-free difference formulation can be applied for the convection one, to which an accurate solution can be obtained. Performance of this process is verified by numerical calculations of some test term and the resulting difference equation can also be problems. Third, two skew exponential difference schemes are proproven to be second-order accurate. However, if the flow posed to raise the solution accuracy in multidimensional problems: velocity is quite large or the grid spacing is not suitably one is designed to be free of numerical diffusion and the other refined, nonphysical spurious oscillation can be found in with minimum numerical diffusion to ensure solution monotonicity.
the resulting solution which reflects erroneous processes
Comparisons with existing schemes are performed by conducting numerical experiments on several test problems. Finally, a simple [1]. This phenomenon is designated as the boundedness blending procedure of these two schemes is suggested to yield problem for the occurrence of an oscillatory solution.
an accurate and stable representation of the convection-diffusion Moreover, difficulties in the convergence may occur if the problem in all possible situations, with or without solution system of equations are solved by an iterative method, such discontinuities.