Search results for " method"

Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

2011

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.

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.

A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets

2011

Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…

A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential …

2002

Abstract In this article, we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations. A series of test examples was solved with these two schemes, different problems with different type of governing equations, and boundary conditions. Particular emphasis was paid to the ability of these schemes to solve the steady-state convection-diffusion equation at high values of the Peclet number. From the examples tested in this work, it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve …

Probing dynamics of dense suspensions: three-dimensional cross-correlation technique

1997

We describe the realization of a novel three-dimensional (3D) cross-correlation scheme, which provides the possibility to measure dynamic structure factors of highly concentrated colloidal samples without contributions of multiply scattered light. The apparatus is easier to align and more compact than the two-colour cross-correlation apparatus, which is commercially available. This should make the 3D cross-correlation set-up more convenient for routine applications, for example in industrial laboratories. We describe the set-up and discuss some special features of the optical components.

Light scattering - diagnostic methods for colloidal dispersions

1993

Abstract The increasing demand from the colloid research community for quick and noninvasive experimental techniques as well as the rapid progress of modern optics and electronics have led to a considerable expansion in the field of light scattering. This review introduces the basic concepts with some emphasis on novel approaches like the study of interacting particle systems, multiple scattering techniques, and non ergodic samples. Particular attention is then devoted to recent experimental progress towards more compact and rugged instruments.

Patterns of rapid weight loss in elite wrestlers

The aim of this study was to examine the methodology used for RWL and to compare different methods and source of influence practiced by various wrestling styles. The obtained results suggest that 67% of athletes had previously lost weight to compete. The wrestling coach represents the most influential person in terms of RWL strategies. The most frequently used methods were increased exercise, gradual dieting, training in heated room and sauna, for all competitors. The education of wrestling coaches is necessary in order to control and decrease the negative impact of RWL.

Pattern Matching and Pattern Discovery Algorithms for Protein Topologies

2001

We describe algorithms for pattern-matching and pattern-learning in TOPS diagrams (formal descriptions of protein topologies). These problems can be reduced to checking for subgraph isomorphism and finding maximal common subgraphs in a restricted class of ordered graphs. We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the given set of data. The maximal common subgraph problem then is solved by repeated subgraph extension and checking for isomorphisms. Despite its apparent inefficiency, this approach yields an algorithm with time complexity proportional to the number of graphs in the input set and is still practical on the given set of data. As a…

Eight-membered Rings with Two Heteroatoms 1,5

2008

The chapter of the third edition of Comprehensive Heterocyclic Chemistry (CHEC III) 12.24 titled ‘Eight-membered Rings with two Heteroatoms 1,5’ deals with diheterocines rings with two heteroatoms in a 1,5 relationship, namely 1,5-diazocine, 1,5-oxazocine, 1,5-thiazocine, 1,5-dioxocin, 1,5-oxathiocin, and 1,5-dithiocin. This chapter covers the literature from 1996 to 2006 and also reports those articles published in 1995 which were not reported in CHEC-II(1996). In this edition, in addition to the uncondensed derivatives, eight-membered 1,5-heterocycles fused to five-, six-, and seven-membered carbocycles or heterocycles are covered. Bridged diheterocines, which actually constitute the majo…

Using Taguchi method for the optimization of processing variables to prepare porous scaffolds by combined melt mixing/particulate leaching

2017

Synthetic biopolymers have made significant inroads into the development of devices for tissue regeneration. In this context, a challenge is the achievement of appropriate properties mimicking the natural extracellular matrix by fabricating scaffolds presenting mechanical properties, specific surface, porosity and pore interconnection adequate for the final application. This study involved a systematic procedure based on Taguchi method for parameters optimization of melt mixing/particulate leaching combined processes aiming to enhance the performance of the scaffolds. In particular, it was evaluated the effect of time and temperature of melt mixing of the poly(lactic acid) matrix with two w…