| Solving ordinary differential problems via the second derivative Legendre polynomials Pseudo-spectral method |
| Paper ID : 1044-ISCHU |
| Authors |
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Hanaa Mousaa1, Mona Fawzy *2, Mamdouh Metwaly Elkady3, Mohamed Ahmed Abdelhakem3 1Department of Mathematics, Faculty of Science, Galala University, Galala City, Egypt 2Basic Science Department, October High Institute for Engineering & Technology (OHI), 6 October, Egypt 3Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| This paper will present a highly efficient technique for solving linear and nonlinear differential problems. We will use the second derivative of Legendre polynomials (SDLPs) via the Pseudo-spectral method. Consequently, we will calculate the SDLPs Gauss-Lobatto quadrature points and Gauss-Lobatto quadrature weights. Then, the differentiation and integration matrices have been constructed into explicit forms. These matrices will be applied to find approximate solutions for ordinary differential equations (ODEs), integro-differential equations (IDEs), and optimal control problems (OCPs). Moreover, algorithms of pseudo-spectral methods for approximating the solution of ODEs, IDEs, and OCPs have been designed. Also, the presented strategy's converge and error analysis are discussed carefully. Finally, our techniques are applied to solve several numerical examples and compared with other methods. These examples include Land-Emden for astrophysics, Bratu for solid fuel ignition mode, Riccati equations, Volterra integro differential equations, and Linear quadratic problems. This example confirms the accuracy and high efficiency of our proposed method. |
| Keywords |
| Second derivative Legendre polynomials, Differentiation matrix, Integration matrix, Ordinary differential equations, Integro-differential equations, Optimal control problems |
| Status: Abstract Accepted (Oral Presentation) |