Asymptotic error expansions for numerical solutions of one-dimensional problems with singularities

Investigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

Numerical Quadrature and Asymptotic Expansions

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

Asymptotic expansions of the error of

We present and analyse a family of fully discrete spline Galerkin methods for the solution of boundary integral equations with logarithmic kernels. Following the analysis of Galerkin methods of a previous paper, we show the existence of asymptotic expansions of the error. In this work we deal with the numerical solution of the integral equation Z 1 0 log jx( ) x(s)j2g(s)ds = u0(s); 8s; where u0...

Asymptotic Formulae for Some One Dimensional Network Flow Problems