Artículos de C.M. García-López en el INSPEC (Ingeniería e Informática) - Papers by - "Garcia-Lopez-CM"

Datos obtenidos el lunes 11 de febrero de 2002

Registro 1 de 8 en INSPEC 1998/07-1998/12

TI: Intermediate boundary conditions in operator-splitting
techniques and linearization methods

AU: Ramos-JI; Garcia-Lopez-CM

SO: Applied-Mathematics-and-Computation. vol.94, no.2-3;
15 Aug. 1998; p.113-36.

PY: 1998

LA: English

AB: The intermediate boundary conditions for the solution
of linear, one-dimensional

reaction-diffusion equations have been determined analytically
for the case that the reaction and

diffusion operators are solved once each in each time
step. These boundary conditions have been

used to solve systems of nonlinear, one-dimensional reaction-diffusion
equations by means of

linearized theta -methods and time-linearized techniques
which are based on the linearization of

the nonlinear algebraic and differential, respectively,
equations of the reaction operator; both

techniques provide analytical solutions to the reaction
operator although in discrete and

continuous forms, respectively. Since the linearization
of reaction operators may result in dense

Jacobian matrices, diagonally and triangularly linearized
techniques which uncouple or couple in a

sequential manner, respectively, the dependent variables
are proposed. It is shown that the

accuracy of time-linearized methods is higher than that
of linearized theta -techniques, whereas the

accuracy of both linearization methods deteriorates as
the coupling between dependent variables is

weakened.

AN: 5993200

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Registro 2 de 8 en INSPEC 1998/01-1998/06

TI: Linearized finite difference methods: application
to nonlinear heat conduction problems

AU: Garcia-Lopez-CM; Ramos-JI

SO: Advanced Computational Methods in Heat Transfer IV.
Comput. Mech. Publications,

Southampton, UK; 1996; 647 pp. p.527-36.

PY: 1996

LA: English

AB: Partially-linearized, approximate factorization methods
for multidimensional, nonlinear

reaction-diffusion problems are presented. These methods
first discretize the time derivatives and

linearize the equations, and then factorize the multidimensional
operators into a sequence of

one-dimensional ones. Depending on how the Jacobian matrix
is approximated, fully coupled,

sequentially coupled or uncoupled, linear, one-dimensional
problems are obtained. It is shown

that the approximate errors of the linearized techniques
presented are nearly the same, whereas

their accuracy depends on the approximation to the Jacobian
matrix.

AN: 5899754

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Registro 3 de 8 en INSPEC 1998/01-1998/06

TI: Comments on a recent paper dealing with the finite-analytic
method

AU: Ramos-JI; Garcia-Lopez-CM

SO: International-Journal-of-Numerical-Methods-for-Heat-&-Fluid-Flow.
vol.7, no.8; 1997;

p.794-800.

PY: 1997

LA: English

AB: The authors refers to Montgomery and Fleeter (see
ibid., vol.6, p.59-77 (1996)) who

employed the finite-analytic method of Chen et al. (1980)
to study steady, two-dimensional,

inviscid, compressible, subsonic flow in a nozzle. The
authors show that, contrary to the statement

made by Montgomery and Fleeter, their boundary conditions
at the computational cell's

boundaries are not constructed from the particular solution
to one of their equations. The authors

deduce from a simple non-linear second-order ordinary
differential equation that the finite or

locally analytic method of Chen et al. (1980) only yields
continuous but not differentiable

solutions. They suggest a finite-analytic method which
provides continuous and differentiable

solutions.

AN: 5865068

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Registro 4 de 8 en INSPEC 7/97-12/97

TI: Nonstandard finite difference equations for ODEs and
1-D PDEs based on piecewise

linearization

AU: Ramos-JI; Garcia-Lopez-CM

SO: Applied-Mathematics-and-Computation. vol.86, no.1;
15 Sept. 1997; p.11-36.

PY: 1997

LA: English

AB: A method for the solution of initial and boundary
value problems in nonlinear, ordinary

differential equations, and for one-dimensional, partial
differential equations which provides

C/sup 1/ solutions is presented. The method is based on
the linearization of the differential

equation in intervals which contain only two grid points
and provides three-point, nonstandard

finite difference equations for the nodal amplitudes.
The method is applied to steady

reaction-diffusion equations, two-point, singularly perturbed
boundary value problems and the

steady Burgers equation, and compared with standard finite
difference and finite element

formulations. For one-dimensional, partial differential
equations, the temporal derivatives are first

discretized, and the resulting ordinary differential equation
accounts for both the temporal and

spatial stiffnesses and is solved by means of piecewise
linearization. Since the linearization

includes a Jacobian matrix, it may be easily employed
to refine the mesh where steep gradients

occur.

AN: 5705319

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Registro 5 de 8 en INSPEC 1/97-6/97

TI: Piecewise-linearized methods for initial-value problems

AU: Ramos-JI; Garcia-Lopez-CM

SO: Applied-Mathematics-and-Computation. vol.82, no.2-3;
15 March 1997; p.273-302.

PY: 1997

LA: English

AB: Piecewise-linearized methods for the solution of initial-value
problems in ordinary differential

equations are developed by approximating the right-hand-sides
of the equations by means of a

Taylor polynomial of degree one. The resulting approximation
can be integrated analytically to

obtain the solution in each interval and yields the exact
solution for linear problems. Three

adaptive methods based on the norm of the Jacobian matrix,
maintaining constant the value of the

approximation errors incurred by the linearization of
the right-hand sides of the ordinary

differential equations, and Richardson's extrapolation
are developed. Numerical experiments with

some nonstiff, first- and second-order, ordinary differential
equations, indicate that the accuracy

of piecewise-linearized methods is, in general, superior
to those of the explicit, modified,

second-order accurate Euler method and the implicit trapezoidal
rule, but lower than that of the

explicit, fourth-order accurate Runge-Kutta technique.
It is also shown that piecewise-linearized

methods do not exhibit computational (i.e., spurious)
modes for the relaxation oscillations of the

van der Pol oscillator, and, for those systems of equations
which satisfy certain conservation

principles, conserve more accurately the invariants than
the trapezoidal rule. An error bound for

piecewise-linearized methods is provided for ordinary
differential equations whose

right-hand-sides satisfy certain Lipschitz conditions.

AN: 5528135

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Registro 6 de 8 en INSPEC 1/97-6/97

TI: Linearized Theta -methods. II. Reaction-diffusion
equations

AU: Garcia-Lopez-CM; Ramos-JI

SO: Computer-Methods-in-Applied-Mechanics-and-Engineering.
vol.137, no.3-4; 15 Nov. 1996;

p.357-78.

PY: 1996

LA: English

AB: Second-order accurate in space, partially-linearized,
triangular and diagonal Theta -methods

for reaction-diffusion equations, which employ either
a standard or a delta formulation, are

developed and applied to both the study of a system of
one-dimensional, reaction-diffusion

equations with algebraic nonlinear reaction terms and
the propagation of a one-dimensional,

confined, laminar flame. These methods require the solution
of tridiagonal matrices for each

dependent variable, and either uncouple or sequentially
couple the dependent variables at each

time step depending on whether they are diagonally- or
triangularly-linearized techniques,

respectively. Partially-linearized, diagonal methods yield
larger errors than partially-linearized,

triangular techniques, and the accuracy of the latter
depends on the time step, standard or delta

formulation, implicitness parameter and the order in which
the equations are solved. Fully- and

partially-linearized, operator-splitting methods for reaction-diffusion
equations are also developed.

The latter provide explicit expressions for the solution
of the reaction operator.

AN: 5459588

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Registro 7 de 8 en INSPEC 1996

TI: A piecewise-linearized method for ordinary differential
equations: two-point boundary value

problems

AU: Garcia-Lopez-CM; Ramos-JI

SO: International-Journal-for-Numerical-Methods-in-Fluids.
vol.22, no.11; 15 June 1996;

p.1089-102.

PY: 1996

LA: English

AB: Piecewise-linearized methods for the solution of two-point
boundary value problems in

ordinary differential equations are presented. These problems
are approximated by piecewise

linear ones which have analytical solutions and reduced
to finding the slope of the solution at the

left boundary so that the boundary conditions at the right
end of the interval are satisfied. This

results in a rather complex system of non-linear algebraic
equations which may be reduced to a

single non-linear equation whose unknown is the slope
of the solution at the left boundary of the

interval and whose solution may be obtained by means of
the Newton-Raphson method. This is

equivalent to solving the boundary value problem as an
initial value one using the

piecewise-linearized technique and a shooting method.
It is shown that for problems characterized

by a linear operator a technique based on the superposition
principle and the piecewise-linearized

method may be employed. For these problems the accuracy
of piecewise-linearized methods is of

second order. It is also shown that for linear problems
the accuracy of the piecewise-linearized

method is superior to that of fourth-order-accurate techniques.
For the linear singular perturbation

problems considered in this paper the accuracy of global
piecewise linearization is higher than that

of finite difference and finite element methods. For non-linear
problems the accuracy of

piecewise-linearized methods is in most cases lower than
that of fourth-order methods but

comparable with that of second-order techniques owing
to the linearization of the non-linear

terms.

AN: 5311432

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Registro 8 de 8 en INSPEC 1996

TI: Linearized Theta -methods. I. Ordinary differential
equations

AU: Ramos-JI; Garcia-Lopez-CM

SO: Computer-Methods-in-Applied-Mechanics-and-Engineering.
vol.129, no.3; 15 Jan. 1996;

p.255-69.

PY: 1996

LA: English

AB: Fully-linearized Theta -methods for autonomous and
non-autonomous, ordinary differential

equations are derived by approximating the non-linear
terms by means of the first-degree

polynomials which result from Taylor`s series expansions.
These methods are implicit but result in

explicit solutions, A-stable, consistent and convergent;
however, they may be very demanding in

terms of both computer time and storage because the matrix
to be inverted is, in general, dense.

The accuracy of fully-linearized Theta -methods is comparable
to that of the standard, implicit,

iterative Theta -methods, and deteriorates as the value
of Theta is decreased from Theta =0.5, for

which both Theta and fully-linearized Theta -methods are
second-order accurate.

Partially-linearized Theta -methods based on the partial
linearization of non-linear terms have also

been developed. These methods result in diagonal or triangular
matrices which may be easily

solved by substitution. Their accuracy, however, is lower
than that of fully-linearized Theta

-methods.

AN: 5233408

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