| Enhanced shifted Tchebyshev Operational Matrix Method for Solving Linear and Nonlinear Telegraph Equations |
| Paper ID : 1042-ISCHU |
| Authors |
|
Mohamed Ahmed Abdelhakem1, Dina Abdel Hamid *2, Mamdouh Metwaly Elkady1, Youssri Hassan Youssri3 1Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt 2Basic science - faculty if Engineering -May university-Cairo-Egypt 3Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt |
| Abstract |
| The Telegraph equation characterizes various phenomena within a range of applied sciences. We use two orthogonal polynomials in this paper; Enhanced shifted Tchebyshev and shifted Tchebyshev. Which fulfill a given set of homogeneous boundary conditions and the necessary formulae have been established. The operation matrix of derivative for Enhanced shifted Tchebyshev and operation matrix of integration for shifted Tchebyshev are applied in these techniques. Then, the presented two polynomials are used together with the two spectral methods, namely, the Galerkin and Tau methods, as the basis functions. the proposed techniques depended on converting the linear/nonlinear telegraph problems and their conditions to an algebraic system of equations. Consequently, this algebraic system will be solved to get the values of spectral expansion’s constants. The convergence and error analyses were introduced and proved. Finally, some illustrative examples of the Telegraph equation have been approximated using the presented method and compared our solutions with other authors. |
| Keywords |
| Telegraph Equations. First-kind Chebyshev polynomials · Galerkin method. Tau method · Error analysis |
| Status: Abstract Accepted (Oral Presentation) |