Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach
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 colloca...
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MDPI AG
2021-08-01
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| author | Mohammad Izadi Şuayip Yüzbaşi Samad Noeiaghdam |
| author_facet | Mohammad Izadi Şuayip Yüzbaşi Samad Noeiaghdam |
| author_sort | Mohammad Izadi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T08:38:15Z |
| format | Article |
| id | doaj.art-956c62f7fac5488f90c3df3eeb57d202 |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-10T08:38:15Z |
| publishDate | 2021-08-01 |
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| series | Mathematics |
| spelling | doaj.art-956c62f7fac5488f90c3df3eeb57d2022023-11-22T08:32:44ZengMDPI AGMathematics2227-73902021-08-01916184110.3390/math9161841Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel ApproachMohammad Izadi0Şuayip Yüzbaşi1Samad Noeiaghdam2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, IranDepartment of Mathematics, Faculty of Science, Akdeniz University, 07058 Antalya, TurkeyDepartment of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, RussiaTwo 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.https://www.mdpi.com/2227-7390/9/16/1841Bessel functionscollocation methoderror boundTroesch’s problemquasi-linearization technique |
| spellingShingle | Mohammad Izadi Şuayip Yüzbaşi Samad Noeiaghdam Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach Mathematics Bessel functions collocation method error bound Troesch’s problem quasi-linearization technique |
| title | Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach |
| title_full | Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach |
| title_fullStr | Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach |
| title_full_unstemmed | Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach |
| title_short | Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach |
| title_sort | approximating solutions of non linear troesch s problem via an efficient quasi linearization bessel approach |
| topic | Bessel functions collocation method error bound Troesch’s problem quasi-linearization technique |
| url | https://www.mdpi.com/2227-7390/9/16/1841 |
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