Desempeño de algunos métodos de Runge-Kutta en la aproximación numérica de la ecuación lineal de Schrödinger
DOI:
https://doi.org/10.31349/RevMexFis.23.010209Keywords:
Schrodinger equation; conservative methods; Runge-Kutta methods; numerical invariantsAbstract
Se comparan diferentes métodos de Runge-Kutta tradicionales aplicados a la ecuación lineal de Schrödinger. Se estudia la conservación de los invariantes fı́sicos relevantes de esta ecuación haciendo uso de un problema escalar elemental, la hermiticidad del operador hamiltoniano y argumentos básicos de álgebra matricial. Además, se discute la estabilidad numérica, solubilidad y selección del paso en tiempo en estos métodos.
Different traditional Runge-Kutta methods applied to the linear Schrödinger equation are compared. The conservation of the relevant physical invariants of this equation is studied using an elementary scalar problem, the hermiticity of the Hamiltonian operator and basic arguments of matrix algebra. In addition, numerical stability, solubility and time step selection for these methods are discussed.
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