| Pseudo Spectral Numerical treatment for some types of differential equations via the second kind chebyshev polynomials |
| Paper ID : 1065-ISCHU |
| Authors |
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Somaya Mahmoud Abdelshahid *1, Mamdouh Metwaly Elkady2, Mohamed Ahmed Abdelhakem2 1Mathematics Department, Faculty of Science,helwan University, Helwan, Cairo, Egypt 2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| A new differentiation technique, fractional pseudo spectral of the second kind of Chebyshev matrices, was introduced. It depends on the second kind of Chebyshev polynomials as a base function. Some properties of second-kind Chebyshev polynomials and recurrence relation are used to get weight functions and the zeros of the Gauss-Lobatto quadrature. We get the weight functions to the Gauss-Lobatto quadrature to Chebyshev of the second kind. We take into consideration its extreme points and inner product. The technique was used to solve ordinary differential equations. Moreover, it extended to approximate integro-differential equations. The novel of second-kind Chebyshev differentiation matrices transformed these ordinary differential problems into an algebraic system of equations. Also, an error and a convergence analysis for that technique were investigated. Finally, the correctness and efficiency of this technique were examined with test functions and several examples. All the results were compared with the results of other methods to ensure the investigated error analysis. |
| Keywords |
| The second kind of Chebyshev, Pseudo-spectral method, Differentiation matrix, Lane-Emden Equation, Reccati Equation, Bratu equation |
| Status: Abstract Accepted (Oral Presentation) |