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CP methods for the Schrödinger equation. (English) Zbl 0971.65067
This paper focuses on a class of piecewise perturbation methods for approximating the potential energy function when solving the one dimensional Schrödinger equation. These methods, known as constant perturbation (CP) methods, approximate the potential energy function by piecewise constants on a set of subintervals and then perform polynomial-type perturbation corrections. An error analysis is given and a simple numerical illustration.

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
Full Text: DOI
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