Numerical methods for an ion transport problem (Q1963922)

The boundary value problem \[ v''+\frac{1}{2}\xi v'+\frac{1}{2}\int_0^{\infty} v(\xi)d\xi h(v)=0,\enskip \xi>0, \] \[ v(0)=1,\enskip v(\infty)=0 \] is considered. This problem arises from a model for ion transport. It is shown that there exists a unique solution. An iterative scheme is proposed and its convergence is proved. The numerical Sinc-Galerkin method for solving the boundary value problem is discussed.