In this paper a new explicit Numerov-type method is introduced. The construction is based on a modification of a sixth-order explicit Numerov-type method recently developed by Tsitouras [Ch. Tsitouras, Explicit Numerov type methods with reduced number of stages, Comput. Math. Appl. 45 (2003) 37–42]. Two free parameters are added in order to nullify the phase-lag and the amplification. The metho...

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrr odinger equation. The formula considered contains certain free parameters which allow it to be tted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well known fourth order Numerov t...

and Applied Analysis 3 Applying the explicit Numerov-type method 2.1 to 2.3 , we obtain the following relation yn 1 − S ( H2 ) yn P ( H2 ) yn−1 0, H λh 2.4

we present a new type of method for the integration of systems of linear inhomogeneous initial value problems with constant coefficients. Our methods are of hybrid explicit Numerov type. The methods are constructed without the intermediate use of high accuracy interpolatory nodes, since only the Taylor expansion at the internal points is needed. Then we derive the order conditions taking advant...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

The Numerov method for linear second-order differential equations is generalized to include equations containing a first derivative term. The method presented has the same degree of accuracy as the ordinary Numerov sixth-order method. A general scheme of the application to the numerical solution of the Hartree-Fock equations is considered.

En este trabajo se presenta una primera aproximación con el propósito de diseñar una arquitectura óptima para la implementación del método de Numerov, el cual permite resolver la Ecuación de Schrödinger Independiente del Tiempo (ESIT) para el caso de una dimensión. El diseño y la simulación han sido realizados mediante el uso de megafunciones de punto flotante de 64 bits disponibles en Quartus ...

Numerov-type ODE Solvers are widely used for the numerical treatment of second order initial value problems. In this work we present a powerful and efficient symbolic code in Mathematica for the derivation of their order conditions and principal truncation error terms. The relative tree theory for such order conditions is presented along with the elements of combinatorial mathematics, partition...