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An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems. (English) Zbl 1487.65192

The authors study a numerical method tailored for solving second-order Airy-type equations. The equation is at first recasted as a first-order system of dimension 2, with a linear term and a nonlinear term. A splitting method with Magnus integrators is then defined for its solution. The proposed method is able to catch relevant features of the solution more efficiently than other methods in the literature, as is reported in the numerical tests.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
65L05 Numerical methods for initial value problems involving ordinary differential equations

Software:

Algorithm 838
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Full Text: DOI

References:

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