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A four-step method for the numerical solution of the Schrödinger equation. (English) Zbl 0705.65050

A new four-step exponentially-fitted method is developed for constructing an interpolation operator L that will integrate exactly the functions \(\exp (\pm wx)\), x exp(\(\pm wx)\), \(x^ 2\exp (\pm wx)\), \(x^ 3\exp (\pm wx)\). The expressions for the coefficients of the method are found such as to ensure the optimal approximation to the eigenvalue Schrödinger equation.
Reviewer: R.S.Dahiya

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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