Abstract:
“Nonstandard” equations (like a nonlinear Schrödinger one) that require very small steps in space and time in numerical computations are considered. Methods for time step increase via hyperbolization, i.e., adding the second time derivative multiplied by a small parameter, are studied. It is shown that the results can be improved by introducing an additional damping term associated with the same small parameter. The limiting values for the relation between the small parameter and the stepsizes in space and time are found.
