Refinement of approximate solutions to a boundary-value problem on a half-line (Q1569396)

The authors consider the refinement of approximate solutions to a boundary value problem for a second-order ordinary differential equation on a half-line. To solve the problem numerically, \([x_{0},\infty)\) is replaced by \([x_{0},R]\), and the boundary condition at \(R\) is derived from the asymptotic form of the solution at infinity. Then, the problem is solved on the segment. The replacement leads to an error. A method for refining approximate solutions to the boundary value problem on a half-line is suggested. The problem is solved for two segments of different length. A refined solution is obtained by extrapolating the solutions obtained along the segment.