| Pseudo-Spectral treatment for some type of differential problems via shifted chebyshev polynomials of the second kind |
| Paper ID : 1032-ISCH |
| Authors |
|
Aya Ahmed Sabry *1, Kamal Raslan Mohamed2, Sahar Hussein Hussein3, Mohamed Ahmed Abdelhakem4 1Teaching assistant at the Higher Institute of Engineering in May 15th 2Math Department, Faculty of Science, Al Azhar university 3College of Science, Department of Mathematics Al-Azhar University (Girls Branch) 4Mathematics Department, Faculty of Science, Helwan University, Helwan 11795, Egypt |
| Abstract |
| In this article, the pseudo-spectral method is used as a technique to employ shifted Chebyshev polynomials of the second kind (SCH-2Sd-Ps) of the well-known Chebyshev polynomials as a novel basis function. That fulfills a given set of homogeneous boundary conditions and establishes the necessary formulas. These orthogonal polynomials are namely shifted Chebyshev polynomials of the second kind. Then, shifted Chebyshev polynomials of the second kind Gauss-Lobatto quadrature weights and zeros have been calculated. Consequently, a matrix for differentiation (D-matrix) is constructed to solve several types of ordinary differential problems. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. The proposed approach differs from other numerical techniques as it is based on the differentiation matrix of shifted Chebyshev polynomials of the second kind. Finally, some integer-order boundary value problems were approximated using the presented method. Also, we compared our results with other techniques to prove the accuracy and efficiency of the proposed technique. |
| Keywords |
| Differential Equations, Spectral methods, pseudo-Spectral methods, Legendre polynomials |
| Status: Abstract Accepted (Poster Presentation) |