Analytical approximation to solutions of singularly perturbed boundary value problems. (English) Zbl 1194.34113
Summary: A computational method is presented for solving a class of nonlinear singularly perturbed two-point boundary value problems with a boundary layer at the left of the underlying interval. First a zeroth order asymptotic expansion for the solution of the given singularly perturbed boundary value problem is constructed. Then the reduced terminal value problem is solved analytically using reproducing kernel Hilbert space method. This method is effective and easy to implement. Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other not only in the boundary layer, but also away from the layer.
MSC:
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
| 34E15 | Singular perturbations for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
