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Nonlinear Schrödinger Equation and the Hyperbolization Method

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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 dam** 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.

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Funding

This work was supported by the Scientific and Educational Mathematical Center of Nizhny Novgorod State University, agreement no. 075-02-2020-1632.

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  1. Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

    A. D. Yunakovsky

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Translated by I. Ruzanova

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Yunakovsky, A.D. Nonlinear Schrödinger Equation and the Hyperbolization Method. Comput. Math. and Math. Phys. 62, 1112–1130 (2022). https://doi.org/10.1134/S0965542522070119

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