Abstract
Two P-stable methods with phase lag of order 10 and 12 are developed in this paper for the numerical integration of the one-dimensional Schrödinger equation. Based on a new local error, the local phase-lag error (LPLE), a new variable-step procedure is produced. Numerical results indicate that the new variable-step method is more efficient than the similar well-known variable-step procedure of Raptis and Cash [Comput. Phys. Commun. 1985, 36, 113–119 (1985)].
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