Compact and Monotone Difference Schemes for the Generalized Fisher Equation

For the generalized Fisher equation with nonlinear convection, monotone and compact difference schemes of $$4+1$$ and $$4+2 $$ approximation orders are constructed and studied on standard stencils with nonstandard relations for the time and space steps. A priori estimates for the difference solution are obtained in the nonlinear case based on the established two-sided estimates for the grid solution. These results are generalized to a two-dimensional generalized Fisher equation with nonlinear convection. The computational experiment conducted illustrates the efficiency of the methods considered.

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