A solution of Chandrasekhar’s integral equation

A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation

The Gross-Pitaevskii equation (GPE), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor proportional to the number of coherent atoms. The square of the wave function, times the above mentioned factor, is defined as the Hartree potential. A method implemented here for the numerical solutio...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

Solution of Hallen's integral equation using multiwavelets

An effective method based upon Alpert multiwavelets is proposed for the solution of Hallen’s integral equation. The properties of Alpert multiwavelets are first given. These wavelets are utilized to reduce the solution of Hallen’s integral equation to the solution of sparse algebraic equations. In order to save memory requirement and computation time, a threshold procedure is applied to obtain ...

A solution of Volterra-Hamerstain integral equation in partially ordered sets

The Solution of a Certain General Type of Integral Equation.

4For n = 1, the nearest approach to the process used here seems to be found in H. J. S. Smith's Report on the Theory of Numbers, Collected Works, Vol. I, 271-272, Oxford (1894); reproduced by P. Bachmann, Die Lehre von der Kreisteilung, 279-281, Leipzig and Berlin (1921). However, our number yt of (1) for n = 1 is not exhibited explicitly by them in terms of the a's alone, but is defined by mea...