A NOVEL-APPROACH TO THE NUMERICAL-SOLUTION OF BOUNDARY-VALUE-PROBLEMSON INFINITE INTERVALS

The classical numerical treatment of two-point boundary value problems on infinite intervals is based on the introduction of a truncated bou ndary (instead of infinity) where appropriate boundary conditions are imposed. Then, the truncated boundary allowing for a satisfactory accu racy is computed by trial. Motivated by several problems of interest i n boundary layer theory, here we consider boundary value problems on i nfinite intervals governed by a third-order ordinary differential equa tion. We highlight a novel approach to define the truncated boundary. The main result is the convergence of the solution of our formulation to the solution of the original problem as a suitable parameter goes t o zero. In the proposed formulation, the truncated boundary is an unkn own free boundary and has to be determined as part of the solution. Fo r the numerical solution of the free boundary formulation, a noniterat ive and an iterative transformation method are introduced. Furthermore , we characterize the class of free boundary value problems that can b e solved noniteratively. A nonlinear how problem involving two physica l parameters and belonging to the characterized class of problems is t hen solved. Moreover, the Falkner-Skan equation with relevant boundary conditions is considered and representative results, obtained by the iterative transformation method, are listed for the Homann flow. All t he obtained numerical results clearly indicate the effectiveness of ou r approach. Finally, we discuss the possible extensions of the propose d approach and for the question of a priori error analysis.