Abstract
AbstractMonotone difference schemes are considered (that is schemes for which the maximum principle holds) for diffusion‐convection problems modelled by (1) or by corresponding parabolic and two‐dimensional elliptic equations. The diffusion/convection ratio may be small or great, and a continuous connection is created between these two cases. For instance, in one of the variants a continuous transition is achieved from the Crank‐Nicholson‐scheme (applied if convection is zero) and a symmetric, second order Wendroff scheme (for the pure transport equation.) Numerical results for (1) show the efficiency of the method.
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