| Chebyshev second kind of pseudo-spectral method for solving integral and differential equations |
| Paper ID : 1019-ISCH |
| Authors |
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Somaya Mahmoud Abdelshahid *1, Mamdouh Metwally Elkady2, Mohamed Ahmed Abdelhakem2 1Modern Academy for Computer Science and Management Technology-Cairo-Egypt 2Mathematics Department, Faculty of Science, Helwan University, Helwan 11795, Egypt |
| Abstract |
| A new differentiation and integration technique, pseudo-spectral of the second kind of Chebyshev matrices, was introduced. It depends on the second kind of Chebyshev polynomials as a base function. We use the trapezoidal numerical method to get the base function. Some properties of second-kind Chebyshev polynomials and recurrence relation are used to get Gauss-Lobatto quadrature weights and the zeros of Gauss-Lobatto quadrature. We take into consideration its extreme points and inner product. The technique was used to solve integral and differential equations. Moreover, it extended to approximate integro- differential equations. The novel of second-kind Chebyshev differentiation and integration 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 those of other methods to ensure the investigated error analysis. |
| Keywords |
| Second kind Chebyshev Polynomials, Pseudo-spectral method, Trapezoidal method, Differential equations, Integral Equation, Reccati Equation, Bratu Equation. |
| Status: Abstract Accepted (Oral Presentation) |