Discretization of Two-Point Boundary Value Problems on an Unbounded Interval by Simplified Operators

The numerical solution of a two-point boundary value problem on an unbounded interval requires an appropriate transformation of the variables or truncation to a finite interval. Here we propose an adapted modification of the asymptotic boundary if the original interval has been truncated. This modification is based on the asymptotic behaviour of the solution which can be obtained by some approximate problem on an infinite interval. The approach is illustrated with specific examples and numerical results are given