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Fourth-order method for singularly perturbed singular boundary value problems using non-polynomial spline |
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| รหัสดีโอไอ | |
| Creator | Kolloju Phaneendra |
| Title | Fourth-order method for singularly perturbed singular boundary value problems using non-polynomial spline |
| Contributor | Emineni Siva Prasad, Diddi Kumara Swamy |
| Publisher | Maejo University |
| Publication Year | 2561 |
| Journal Title | Maejo International Journal of Science and Technology |
| Journal Vol. | 12 |
| Journal No. | 1 |
| Page no. | 1 |
| Keyword | singularly perturbed two-point singular boundary value problem, interior nodes, singular point, non-polynomial spline, boundary layer |
| Website title | Maejo International Journal of Science and Technology |
| ISSN | 1905-7873 |
| Abstract | This paper envisages a fourth-order finite difference method with reference to the solution of a class of singularly perturbed singular boundary value problems especially on a uniform mesh. The non-polynomial spline forms the tool for the solution of the problems. The discretisation equation of the problems are developed using the condition of continuity for the first-order derivatives of the non- polynomial spline at the interior nodes and it is not valid at the singularity. Hence at the singularity, the boundary value problem is modified in order to get a three-term relation. The tridiagonal scheme of the method is processed using discrete invariant imbedding algorithm. The convergence of the method is analysed and maximum absolute errors in the solution are tabulated. Root mean square errors in the solution of the examples are presented in comparison to the methods chosen from the literature to establish the proposed method. |
