Approximating Solutions of Non-Linear Troesch's Problem via an Efficient Quasi-Linearization Bessel Approach
MATHEMATICS, vol.9, no.16, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 9 Issue: 16
- Publication Date: 2021
- Doi Number: 10.3390/math9161841
- Journal Name: MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Keywords: Bessel functions, collocation method, error bound, Troesch's problem, quasi-linearization technique, COLLOCATION METHOD, ALGORITHM, PLASMA
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch's problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iteratively. In the latter approach, we require to solve a linear algebraic matrix equation in each iteration. Moreover, the error analysis of the Bessel series solution is established. In the end, numerical simulations and computational results are provided to illustrate the utility and applicability of the presented collocation approaches. Numerical comparisons with some existing available methods are performed to validate our results.