Artículos de F.R. Villatoro en el INSPEC (Ingeniería e Informática) - Papers by - "VILLATORO-FR"

Datos obtenidos el lunes 11 de febrero de 2002

Registro 1 de 10 en INSPEC 2001/01-2001/08

TI: Solitons in nonlinear waveguides with sinusoidal Kerr-index

AU: Villatoro-FR; Ramos-JI

SO: ISRAMT'99. 1999 7th International Symposium on Recent
Advances in Microwave

Technology Proceedings. ISRAMT, Spain; 1999; iii+801 pp.
p.41-4.

PY: 1999

LA: English

AB: The effect of a nonlinear optical medium with a sinusoidal
variation of the Kerr refraction

index on the propagation of solitons is studied numerically
by means of a linearized theta -method.

Both the width and wavelength of the sinusoidal variation
and the width of the soliton determine

whether the soliton will be trapped in or pass through
the region where the sinusoidal variation

occurs. In both cases, the soliton radiates energy upstream
and downstream. The effect of linear

losses is small and does not alter the main characteristics
of the interaction of the soliton with the

periodically nonlinear medium.

AN: 6957075

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Registro 2 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. VI. Asymptotic
analysis of and asymptotic

successive-corrections techniques for two-point, boundary-value
problems in ODE's

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.105, no.2-3;
Nov. 1999; p.137-71.

PY: 1999

LA: English

AB: The modified equation technique is extended to two-point,
boundary-value problems, and a

second-order accurate, implicit, centered, finite difference
scheme for nonhomogeneous,

second-order, ordinary differential equations with linear
boundary conditions is analyzed. The

first, second and third modified equations, or equivalent,
second equivalent and (simply) modified

equations, respectively, for this scheme and its boundary
conditions are presented. It is shown that

the three kinds of modified equations are asymptotically
equivalent when the equivalent equation

is used for the boundary conditions, since an asymptotic
analysis of these equations with the grid

size as small parameter yields exactly the same results.
For a linear problem, multiple scales and

summed-up asymptotic techniques are used and the resulting
uniform asymptotic expansions are

shown to be equivalent to the solution of the original
finite difference scheme. Asymptotic

successive-corrections techniques are also applied to
the three kinds of modified equations to

obtain higher-order schemes. Higher-order boundary conditions
are easily treated in the

asymptotic successive-corrections technique, although
these boundary conditions must be

obtained by using the equivalent equation in order to
obtain a correct estimate of the global error

near the domain boundaries. The methods introduced in
this paper are applied to homogeneous

and non-homogeneous, second-order, linear and non-linear,
ordinary differential equations, and

yield very accurate results.

AN: 6392069

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Registro 3 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. V. Asymptotic
analysis of and direct-correction and

asymptotic successive-correction techniques for the implicit
midpoint method

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.241-85.

PY: 1999

LA: English

AB: For pt.IV. see ibid., p. 213-40. The equivalent, second
equivalent and (simply) modified

equations for the implicit midpoint rule are shown to
be asymptotically equivalent in the sense that

an asymptotic analysis of these equations with the time
step size as small parameter yields exactly

the same results; for linear problems with constant coefficients,
they are also equivalent to the

original finite difference scheme. Straight forward (regular),
multiple scales and summed-up

asymptotic techniques are used for the analysis of the
implicit midpoint rule difference method,

and the accuracy of the resulting asymptotic expansion
is assessed for several first-order,

non-linear, autonomous ordinary differential equations.
It is shown that, when the resulting

asymptotic expansion is uniformly valid, the asymptotic
method yields very accurate results if the

solution of the leading order equation is smooth and does
not blow up. The modified equation is

also studied as a method for the development of new numerical
schemes based on both

direct-correction and asymptotic successive-correction
techniques applied to the three kinds of

modified equations, the linear stability of these techniques
is analyzed, and their results are

compared with those of Runge-Kutta schemes for several
autonomous and non-autonomous,

first-order, ordinary differential equations.

AN: 6296085

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Registro 4 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. IV. Numerical
techniques based on the modified

equation for the Euler forward difference method

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.213-40.

PY: 1999

LA: English

AB: The modified equation method is studied as a technique
for the development of new

numerical techniques for ordinary differential schemes
based on the third modified or (simply)

modified equation of the explicit Euler forward method.
Both direct-correction and

successive-correction techniques based on the modified
equation are used to obtain higher-order

schemes. The resulting numerical techniques are completely
explicit, of order of accuracy as high

as desired, and self-starting since the truncation error
terms in the modified equation have no

derivatives. The methods introduced in this paper are
applied to autonomous and

non-autonomous, scalar and systems of ordinary differential
equations and compared with

second- and fourth-order accurate Runge-Kutta schemes.
It is shown that, for sufficiently small

step sizes, the fourth-order direct-correction and successive-correction
methods are as accurate as

the fourth-order Runge-Kutta scheme.

AN: 6296084

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Registro 5 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. III. Numerical
techniques based on the second

equivalent equation for the Euler forward difference method

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.179-212.

PY: 1999

LA: English

AB: For pt.II. see ibid., p. 141-178. Direct-correction
and asymptotic successive-correction

methods based on the second equivalent equation are applied
to the Euler forward explicit

scheme. In direct-correction, the truncation error terms
of the second equivalent equation which

contain higher-order derivatives together with a starting
procedure, are discretized by means of

finite differences. Both explicit and implicit direct-correction
schemes are presented and their

stability regions are studied. The asymptotic successive-correction
numerical technique developed

in Part II of this series with a consistent starting procedure
is applied to the second equivalent

equation. Both all-backward and all-centered asymptotic
successive-correction methods are

presented. The numerical methods introduced in this paper
are applied to autonomous and

non-autonomous, scalar and systems of ordinary differential
equations and compared with the

results of second- and fourth-order accurate Runge-Kutta
methods. It is shown that the

fourth-order Runge-Kutta method is more accurate than
the successive-correction techniques for

large time steps due to the need for higher-order derivatives
of the Euler solution; however, for

sufficiently small time steps, but larger enough so that
round-off errors are negligible, both

methods have nearly the same accuracy.

AN: 6296083

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Registro 6 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. II: Numerical
techniques based on the equivalent

equation for the Euler forward difference method

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.141-77.

PY: 1999

LA: English

AB: For pt.I. see ibid., p. 111-39. New numerical successive-correction
techniques for ordinary

differential equations based on the Euler forward explicit
method and the first modified or

equivalent equation are presented. These techniques are
similar to iterative updating deferred

methods and are based on the application of asymptotic
methods to modified equations which do

not require initial conditions for the high order derivatives
in the truncation terms and which yield

stable numerical methods. It is shown that, depending
on the discretization of the high order

derivatives in the high order correction equations, different
methods of as high order of

consistency as required can be developed. In this paper,
backward and centered formulas are

used, but the resulting numerical methods are not self-starting.
It is shown that, if the starting

procedure is not adequate, the numerical order of the
method can be smaller than the theoretical

one. In order to avoid this loss of numerical order, a
method for consistently starting the

asymptotic successive-correction technique based on the
use of fictitious times is presented and

applied to autonomous and nonautonomous, ordinary differential
equations, and compared with

the results of second and fourth-order Runge-Kutta methods.
It is shown that the fourth-order

Runge-Kutta method is more accurate than the successive-correction
techniques for large time

steps due to the higher order derivatives in the successive-correction,
but, for sufficiently small

time steps, these techniques have almost the same accuracy
as the fourth-order Runge-Kutta

method.

AN: 6296082

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Registro 7 de 10 en INSPEC 1999/01-1999/10

TI: On the method of modified equations. I. Asymptotic
analysis of the Euler forward difference

method

AU: Villatoro-FR; Ramos-JI

SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.111-39.

PY: 1999

LA: English

AB: The method of modified equations is studied as a technique
for the analysis of finite

difference equations. The non-uniqueness of the modified
equation of a difference method is

stressed and three kinds of modified equations are introduced.
The first modified or equivalent

equation is the natural pseudo-differential operator associated
to the original numerical method.

Linear and nonlinear combinations of the equivalent equation
and their derivatives yield the

second modified or second equivalent equation and the
third modified or (simply) modified

equation, respectively. For linear problems with constant
coefficients, the three kinds of modified

equations are equivalent among them and to the original
difference scheme. For nonlinear

problems, the three kinds of modified equations are asymptotically
equivalent in the sense that an

asymptotic analysis of these equations with the time step
as small parameter yields exactly the

same results. In this paper, both regular and multiple
scales asymptotic techniques are used for the

analysis of the Euler forward difference method, and the
resulting asymptotic expansions are

verified for several nonlinear, autonomous, ordinary differential
equations. It is shown that, when

the resulting asymptotic expansion is uniformly valid,
the asymptotic method yields very accurate

results if the solution of the leading order equation
is smooth and does not blow up, even for large

step sizes.

AN: 6296081

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Registro 8 de 10 en INSPEC 1993-1994

TI: Classical forces on solitons in finite and infinite
nonlinear planar waveguides

AU: Ramos-JI; Villatoro-FR

SO: Microwave-and-Optical-Technology-Letters. vol.7, no.13;
Sept. 1994; p.620-5.

PY: 1994

LA: English

AB: Conservation equations for the mass, linear momentum,
and energy densities of solitons

propagating in finite, infinite, and periodic nonlinear
planar waveguides and governed by the

nonlinear Schrodinger equation are derived. These conservation
equations are used to determine

classical force densities that are compared with those
derived by drawing a quantum mechanics

analogy between the propagation of solitons and the motion
of a quantum particle in a nonlinear

potential well.

AN: 4821659

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Registro 9 de 10 en INSPEC 1993-1994

TI: A quantum mechanics analogy for the nonlinear Schrodinger
equation in the finite line

AU: Ramos-JI; Villatoro-FR

SO: Computers-&-Mathematics-with-Applications. vol.28,
no.4; Aug. 1994; p.3-17.

PY: 1994

LA: English

AB: A quantum mechanics analogy is used to determine the
forces acting on and the energies of

solitons governed by the nonlinear Schrodinger equation
in finite intervals with periodic and with

homogeneous Dirichlet, Neumann and Robin boundary conditions.
It is shown that the energy

densities remain nearly constant for periodic, while they
undergo large variations for

homogeneous boundary conditions. The largest variations
in the force and energy densities occur

for the Neumann boundary conditions, but, for all the
boundary conditions considered, the

magnitudes of these forces and energies recover their
values prior to the interaction of the soliton

with the boundary, after the soliton rebound process is
completed. It is also shown that the

quantum momentum changes sign but recovers its original
value after the collision of the soliton

with the boundaries. The asymmetry of the Robin boundary
conditions shows different dynamic

behaviour at the left and right boundaries of the finite
interval.

AN: 4736811

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Registro 10 de 10 en INSPEC 1993-1994

TI: Forces on solitons in finite, nonlinear, planar waveguides

AU: Ramos-JI; Villatoro-FR

SO: Microwave-and-Optical-Technology-Letters. vol.7, no.8;
5 June 1994; p.378-81.

PY: 1994

LA: English

AB: The forces acting on and the energies of solitons
governed by the nonlinear Schrodinger

equation in finite planar waveguides with periodic and
with homogeneous Dirichlet, Neumann,

and Robin boundary conditions are determined by means
of a quantum analogy. It is shown that

these densities have S-shaped profiles and increase as
the hardness of the boundary conditions

increases.

AN: 4693674

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