The Numerical Study of Blowup with Application to a Nonlinear Schrödinger Equation

Abstract We discuss the use of numerical methods in the study of the solutions of evolution problems which exhibit finite-time unbounded growth. We first examine a naive approach in which the growth rate of the numerical solution is accepted as an approximation of the true growth rate. As we shall demonstrate for a radial nonlinear Schrodinger equation, this approach is inadequate since different discretizations exhibit different growth rates. The spurious behaviour of discretizations in the neighbourhood of the singularity is discussed. A reliable procedure for the estimation of the blowup parameters is considered which eliminates the discrepancies between different numerical methods.

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