| Legendre mth derivatives Pseudo-spectral matrices for solving differential equations |
| Paper ID : 1020-ISCH |
| Authors |
|
mona Fawzy Ibrahim *1, Mamdouh Metwally Elkady2, Mohamed Ahmed Abdelhakem2 1Basic Science Department, October High Institute for Engineering & Technology (OHI), 6 October, Egypt 2Mathematics Department, Faculty of Science, Helwan University, Helwan 11795, Egypt |
| Abstract |
| In this study, we will investigate a highly efficient technique for solving linear and nonlinear differential equations. We will use the mth derivative of Legendre polynomials (MDLPs) as a new base function via the Pseudo-spectral method. Consequently, we will first calculate Gauss-Lobatto quadrature points and Gauss-Lobatto quadrature weights for MDLPs. Then, an explicit form of the differentiation matrix has been constructed. This matrix has been employed to approximate solutions for ordinary differential equations (ODEs). Moreover, the pseudo-spectral algorithm for approximating the solution of ordinary differential equations (ODEs) has been designed. Also, the presented strategy’s converge and error analysis are discussed carefully. Additionally, our technique was 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, and real-life applications for fluid flow. Finally, the accuracy, efficiency, and high stability of our presented method have been shown. |
| Keywords |
| mth derivative Legendre polynomials, Pseudo-spectral method, Differentiation matrix, Ordinary differential equations, Lane–Emden equation, Riccati Equation, Bratu equation |
| Status: Abstract Accepted (Poster Presentation) |