On the numerical solution of a class of nonstandard Sturm–Liouville boundary value problems

摘要

The paper deals with the numerical solution of a nonstandard Sturm–Liouville boundary value problem on the half line where the coefficients of the differential terms depend on the unknown function by means of a scalar integral operator. By using a finite difference discretization, a truncated quadrature rule and an iterative procedure, we construct a numerical method, whose convergence is proved. The order of convergence and the truncation at infinity are also discussed. Finally, some numerical tests are given to show the performance of the method.