Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics
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2015-01-01
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© 2015 International Press.We study the Strang splitting scheme for quasilinear Schrödinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to the analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests are performed for a modified version of the superfluid thin film equation.
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Lu, J, and JL Marzuola (2015). Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics. Communications in Mathematical Sciences, 13(5). pp. 1051–1074. 10.4310/CMS.2015.v13.n5.a1 Retrieved from https://hdl.handle.net/10161/14100.
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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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