Search results for "Applied Mathematics"

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…

The $Q_{ \alpha}$-restriction problem

2019

When is a 𝑝-block a 𝑞-block?

1997

Let p p and q q be distinct prime numbers and let G G be a finite group. If B p B_{p} is a p p -block of G G and B q B_{q} is a q q -block, we study when the set of ordinary irreducible characters in the blocks B p B_{p} and B q B_{q} coincide.

Über den Rang der projektiven Darstellung von Kettengeometrien auf Grassmann-Mannigfaltigkeiten

1985

Zur Existenz von Lösungen gewisser Randwertaufgaben

1971

With the aid of some known results about integral equations of the Hammerstein type there is proofed an existence theorem for the following class of boundary value problems−y″−l 2 y′=f(x,y),y(a)=y(b)=0,l 2>0 mit|f(x, y)|=0,l 3 (x)>0. The existence range is determined by the greatest eigenvalue of some linear problem.

Metric properties of the group of area preserving diffeomorphisms

2001

Area preserving cliffeoinorpliisms of the 2-disk which are identity near the boundary form a group D2 wllich can be equipped, usin-g tlhe L2nlorm on its Lie algebra, with a right invariant metric. Witll tllis metric the diameter of D2 is infinite. In this paper we sl-iow that D2 contains quasiisometric embeddings of any finitely generated free group and any finitely generated abelian free group.

Explicit Upper Bound for Entropy Numbers

2004

We give an explicit upper bound for the entropy numbers of the embedding I : W r,p(Ql) → C(Ql) where Ql = (−l, l)m ⊂ Rm, r ∈ N, p ∈ (1,∞) and rp > m.

Parametrization of Sum‐Of‐Sinusoids Channel Models

2011