The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green’s functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not on...

Maximum principle or positivity-preserving property holds for many mathematical 5 models. When the models are approximated numerically, it is preferred that these important prop6 erties can be preserved by numerical discretizations for the robustness and the physical relevance of 7 the approximate solutions. In this paper, we investigate such discretizations of high order accuracy 8 within the ...

In this paper we present a posteriori error estimators for the approximate solutions of linear parabolic equations. We consider discretizations of the problem by discontinuous Galerkin method in time corresponding to variant Crank-Nicolson schemes and continuous Galerkin method in space. Especially, £nite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson...

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

Spherical radial basis functions are used to define approximate solutions to strongly elliptic and elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.

Abstract. Spherical radial basis functions are used to define approximate solutions to pseudodifferential equations of negative orders on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the collocation method. A salient feature of our approach in this paper is a simple error analysis for the collocation method using the same argument as that for the G...

We reformulate the Johnson–Nedelec approach for the exterior two-dimensional Stokes problem taking advantage of the parameterization of the artificial boundary. The main aim of this paper is the presentation and analysis of a fully discrete numerical method for this problem. This one responds to the needs of having efficient approximate quadratures for the weakly singular boundary integrals. We...

In the present paper we consider the fully discrete wavelet Galerkin scheme for the fast solution of boundary integral equations in three dimensions. It produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. We focus on algorithmical details of the scheme, in part...

Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.

This paper uses the Galerkin method to find approximate solutions of some boundary value problems. The solving process requires solve a system algebraic equations, which are large and difficult be solved. According Groebner bases theory, an improved Buchberger's algorithm is proposed system. results show that approach simple efficient.