Abstract
The main goal of this chapter is to discuss the numerical solution of nonlinear wave equations associated with the first of the celebrated Painlevé transcendent ordinary differential equations and the Bratu problem nonlinearity. In order to solve numerically the above equations, whose solutions blow up in finite time in most cases, we advocate a numerical methodology based on the Strang’s symmetrized operator-splitting scheme. With this approach, we can decouple nonlinearity and differential operators. The resulting schemes, combined with a finite element space discretization and adaptive time-stepping to monitor possible blow-up of the solution, provide a robust and accurate solution methodology, as shown by the results of the numerical experiments reported here.
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Quaini, A., Glowinski, R. (2016). Splitting Methods for Some Nonlinear Wave Problems. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_20
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DOI: https://doi.org/10.1007/978-3-319-41589-5_20
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