Search results for "Method"

Third-order iterative methods without using any Fréchet derivative

2003

AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.

The rate of multiplicity of the roots of nonlinear equations and its application to iterative methods

2015

Nonsimple roots of nonlinear equations present some challenges for classic iterative methods, such as instability or slow, if any, convergence. As a consequence, they require a greater computational cost, depending on the knowledge of the order of multiplicity of the roots. In this paper, we introduce dimensionless function, called rate of multiplicity, which estimates the order of multiplicity of the roots, as a dynamic global concept, in order to accelerate iterative processes. This rate works not only with integer but also fractional order of multiplicity and even with poles (negative order of multiplicity).

Parallel finite element splitting-up method for parabolic problems

1991

An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.

A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm

2014

Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.

A Spline Collocation Scheme for the Spherical Shallow Water Equations

1999

On finite element approximation of the gradient for solution of Poisson equation

1981

A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.

Iterative approximation to a coincidence point of two mappings

2015

In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.

OPKINE, a multipurpose program for kinetics

1991

The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A …

Shooting methods for 1D steady-state free boundary problems

1993

AbstractIn this note, we present two numerical methods based on shooting methods to solve steady-state diffusion-absorption models.

An automatic L1-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks

2023

Fast Field-Cycling Nuclear Magnetic Resonance relaxometry is a non-destructive technique to investigate molecular dynamics and structure of systems having a wide range of ap- plications such as environment, biology, and food. Besides a considerable amount of liter- ature about modeling and application of such technique in specific areas, an algorithmic approach to the related parameter identification problem is still lacking. We believe that a robust algorithmic approach will allow a unified treatment of different samples in several application areas. In this paper, we model the parameters identification problem as a con- strained L 1 -regularized non-linear least squares problem. Following…