A New Methodology for the Development of Numerical Methods for the Numerical Solution of the Schrödinger Equation
For researchers solving the Schrödinger equation, this offers a new approach to improve numerical accuracy, though it appears incremental as it builds on existing phase-lag concepts.
The paper introduces a methodology for constructing numerical methods for the one-dimensional Schrödinger equation by requiring vanishing phase-lag and its derivatives, with efficiency demonstrated through error analysis and numerical applications.
In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schrödinger equation. The new methodology is based on the requirement of vanishing the phase-lag and its derivatives. The efficiency of the new methodology is proved via error analysis and numerical applications.