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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