Bernstein basis functions based algorithm for solving system of third order initial value problems
| Autor: | Emad E. Mahmoud, Kottakkaran Sooppy Nisar, Abdul Ghaffar, Muhammad Basit, Masnour S.M. Lotayif, Rida Malik, Faheem Khan |
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| Rok vydání: | 2021 |
| Předmět: |
Operational matrices
Discretization Iterative method Differential equation Chebyshev nodes 020209 energy Collocation points MathematicsofComputing_NUMERICALANALYSIS General Engineering Basis function Bernstein polynomials 02 engineering and technology Engineering (General). Civil engineering (General) 01 natural sciences Bernstein polynomial 010305 fluids & plasmas Algebraic equation Ordinary differential equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Initial value problem Applied mathematics ODEs TA1-2040 |
| Zdroj: | Alexandria Engineering Journal, Vol 60, Iss 2, Pp 2395-2404 (2021) |
| ISSN: | 1110-0168 |
| DOI: | 10.1016/j.aej.2020.12.036 |
| Popis: | For obtaining numerical solutions of the system of ordinary differential equations (ODEs) of third order, a new numerical technique is proposed by using operational matrices of Bernstein polynomials. These operational matrices can be utilized to solve different problems of integral and differential equations. The System of third-order ODEs occur in various physical and engineering models. In this paper, an iterative algorithm is constructed by using operational matrices of Bernstein polynomials for solving the system of third order ODEs. The proposed technique provides a numerical solution by discretizing the system to a system of algebraic equations which can be solved directly. The method will be verified by using appropriate examples which are arising in Physics and some Engineering problems. The comparison of approximate and exact solution of the given examples is demonstrated with the help of tables and graphs. |
| Databáze: | OpenAIRE |
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