| Modified Shifted Third Kind Chebyshev Polynomials for Solving Fraction Boundary Value Problems |
| Paper ID : 1025-ISCH |
| Authors |
|
Peter Salah Nageh *1, Mamdouh Metwally Elkady2, Dina Abdelhamied3, Mohamed Ahmed Abdelhakem2 1Basic science - faculty of computer science - Modern academy 2Mathematics Department, Faculty of Science, Helwan University, Helwan 11795, Egypt 3Dr- Basic science-faculty of Engineering -May University in Cairo |
| Abstract |
| New orthogonal polynomials have been generated from shifted Chebyshev polynomials of the third kind (SCH-3rd-Ps) that fulfill a given set of homogeneous boundary conditions and the necessary formulae have been established. These orthogonal polynomials are namely Modified shifted Chebyshev third-kind polynomials (MSCH-3rd-Ps). Some essential relations are generated for these proposed polynomials. Moreover, a fraction order derivative operational matrix has been introduced. Then, the presented novel polynomials are used together with the spectral methods, namely, the Galerkin methods, as the basis functions to find the approximate solutions. This technique presents these solutions as a finite sum of the proposed polynomials and unknown coefficients. Finally, some fraction-order boundary value problems (F-BVPs) have been approximated using the presented method (Galerkin methods). We also compared our results with other techniques to prove the accuracy and efficiency of the proposed technique. Fraction boundary value problems (FBVPs) in some applications are solved by the proposed techniques in this paper. |
| Keywords |
| Chebyshev Third-kind polynomials, Spectra Method, Galerkin method |
| Status: Abstract Accepted (Poster Presentation) |