Search results for "Approximate solution"

Best proximity point theorems for proximal cyclic contractions

2017

The purpose of this article is to compute a global minimizer of the function $$x\longrightarrow d(x, Tx)$$ , where T is a proximal cyclic contraction in the framework of a best proximally complete space, thereby ensuring the existence of an optimal approximate solution, called a best proximity point, to the equation $$Tx=x$$ when T is not necessarily a self-mapping.

Collocation Method for Linear BVPs via B-spline Based Fuzzy Transform

2018

The paper is devoted to an application of a modified F-transform technique based on B-splines in solving linear boundary value problems via the collocation method. An approximate solution is sought as a composite F-transform of a discrete function (which allows the solution to be compactly stored as the values of this discrete function). We demonstrate the effectiveness of the described technique with numerical examples, compare it with other methods and propose theoretical results on the order of approximation when the fuzzy partition is based on cubic B-splines.

Best proximity point theorems for rational proximal contractions

2013

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

Computing continuous numerical solutions of matrix differential equations

1995

Abstract In this paper, we construct analytical approximate solutions of initial value problems for the matrix differential equation X ′( t ) = A ( t ) X ( t ) + X ( t ) B ( t ) + L ( t ), with twice continuously differentiable functions A ( t ), B ( t ), and L ( t ), continuous. We determine, in terms of the data, the existence interval of the problem. Given an admissible error e, we construct an approximate solution whose error is smaller than e uniformly, in all the domain.

Test of the semischematic model for a liquid of linear molecules

1998

We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].

Indicators of Errors for Approximate Solutions of Differential Equations

2014

Error indicators play an important role in mesh-adaptive numerical algorithms, which currently dominate in mathematical and numerical modeling of various models in physics, chemistry, biology, economics, and other sciences. Their goal is to present a comparative measure of errors related to different parts of the computational domain, which could suggest a reasonable way of improving the finite dimensional space used to compute the approximate solution. An “ideal” error indicator must possess several properties: efficiency, computability, and universality. In other words, it must correctly reproduce the distribution of errors, be indeed computable, and be applicable to a wide set of approxi…

Approximate solutions for two-level optimization problems

1988

This paper is devoted to general results for approximating two-level optimization problems in which the set of solutions to the lower level problem is not a singleton.

Common best proximity points and global optimal approximate solutions for new types of proximal contractions

2015

Let $(\mathcal{X},d)$ be a metric space, $\mathcal{A}$ and $\mathcal{B}$ be two non-empty subsets of $\mathcal{X}$ and $\mathcal{S},\mathcal{T}: \mathcal{A} \to \mathcal{B}$ be two non-self mappings. In view of the fact that, given any point $x \in \mathcal{A}$, the distances between $x$ and $\mathcal{S}x$ and between $x$ and $\mathcal{T}x$ are at least $d(\mathcal{A}, \mathcal{B}),$ which is the absolute infimum of $d(x, \mathcal{S} x)$ and $d(x, \mathcal{T} x)$, a common best proximity point theorem affirms the global minimum of both the functions $x \to d(x, \mathcal{S}x)$ and $x \to d(x, \mathcal{T}x)$ by imposing the common approximate solution of the equations $\mathcal{S}x = x$ and $…

On an approximate solution of fractionally damped dynamical systems

2011