A new method for computation of eigenvalues of the radial Schrödinger operator $-d^2/d{x}^2+v\left(x\right),x\ge 0$ is presented. The potential $v\left(x\right)$ is assumed to behave as $x^{-2+ϵ}$ if $x\to 0_{+}$ and as $x^{-2-ϵ}$ if $x\to +\infty ,ϵ\ge 0$. The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function $z(x,\aleph )$. It is shown that the eigenvalues are the discontinuity points of the function $z(\infty ,\aleph )$. Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is $1/2$ in general and $1$ when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl’s rheological model, our estimates in maximum norm do not depend on spatial dimension.

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension. ...