Abstract
A new way for constructing efficient embedded modified Runge–Kutta methods for the numerical solution of the Schrödinger equation is presented in this paper. The methods of the embedded scheme have algebraic orders five and four. Applications of the new pair to the elastic scattering phase-shift problem and coupled differential equations of Schrödinger type indicate that the new pair is much more efficient than other well known comparable embedded Runge–Kutta pairs.
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