Browsing by Subject "Laplace transforms"
Now showing items 119 of 19

Article
An analytical method for linear elliptic PDEs and its numerical implementation
(2004)A new numerical method for solving linear elliptic boundary value problems with constant coefficients in a polygonal domain is introduced. This method produces a generalized DirichletNeumann map: given the derivative of ...

Article
Boundary value problems for quasilinear ODEs
(2005)A priori bounds for the quasilinear ordinary differential equations (ODE), are discussed. A priori bounds for the derivative of the solution of onedimensional pLaplacian are proved. The global solvability of quasilinear ...

Article
Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
(2008)In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace's equation which are defined in simplyconnected domains into harmonic Dirichlet problems that are defined in the unit disk. We ...

Article
Laplace type invariants for variable coefficient mKdV equations
(2015)We consider a class of variablecoefficient mKdV equations. We derive the equivalence transformations in the infinitesimal form and we employ them to construct differential invariants of the respective equivalence algebra. ...

Article
A matrix decomposition MFS algorithm for axisymmetric potential problems
(2004)The method of fundamental solutions is a boundarytype meshless method for the solution of certain elliptic boundary value problems. By exploiting the structure of the matrices appearing when this method is applied to ...

Article
A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
(2006)In this work we apply the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation to certain axisymmetric harmonic and biharmonic problems. By exploiting the block circulant structure of the ...

Conference Object
Performance of GMRES for the MFS
(2009)In this work we present some preliminary numerical results regarding the performance of the Generalized Minimal Residual (GMRES) method when it is applied to the solution of the linear systems arising from the discretization ...

Article
Random spectral measure for non Gaussian moving averages
(2017)We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh ...

Article
Simultaneous numerical determination of a corroded boundary and its admittance
(2015)In this paper, an inverse geometric problem for Laplace’s equation arising in boundary corrosion detection is considered. This problem, which consists of determining an unknown corroded portion of the boundary of a bounded ...

Article
The singular function boundary integral method for 3D Laplacian problems with a boundary straight edge singularity
(2012)Threedimensional Laplace problems with a boundary straightedge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...

Article
The singular function boundary integral method for a twodimensional fracture problem
(2006)The singular function boundary integral method (SFBIM) originally developed for Laplacian problems with boundary singularities is extended for solving twodimensional fracture problems formulated in terms of the Airy stress ...

Conference Object
The singular function boundary integral method for Laplacian problems with boundary singularities in two and threedimensions
(2010)We present a Singular Function Boundary Integral Method (SFBIM) for solving elliptic problems with a boundary singularity. In this method the solution is approximated by the leading terms of the asymptotic solution expansion, ...

Article
The Singular Function Boundary Integral Method for singular Laplacian problems over circular sections
(2010)The Singular Function Boundary Integral Method (SFBIM) for solving twodimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic ...

Article
A singular function boundary integral method for the laplace equation
(1996)The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic ...

Article
Solving Laplacian problems with boundary singularities: A comparison of a singular function boundary integral method with the p/hp version of the finite element method
(2005)We solve a Laplacian problem over an Lshaped domain using a singular function boundary integral method as well as the p/hp finite element method. In the former method, the solution is approximated by the leading terms of ...

Article
Some aspects of the Method of Fundamental Solutions for certain harmonic problems
(2001)The Method of Fundamental Solutions (MFS) is a boundarytype method for the solution of certain elliptic boundary value problems. The basic ideas of the MFS were introduced by Kupradze and Alexidze and its modern form was ...

Article
Spectral density and spectral distribution inference for long memory time series via fixedb asymptotics
(2014)This paper studies taperbased estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow ...

Article
Threedimensional image reconstruction using the PF/MFS technique
(2009)We propose a geometric modeling method in R3 based on the socalled potential field (PF) modeling technique. The method is a new technique for surface reconstruction from a data set of scattered points taken on a surface. ...

Article
The underdetermined version of the MFS: Taking more sources than collocation points
(2010)In this study we investigate the approximation of the solutions of certain elliptic boundary value problems by the Method of Fundamental Solutions (MFS). In particular, we study the case in which the number of singularities ...