| Solving real-life bvps via the second derivative Chebyshev pseudo-Galerkin method |
| Paper ID : 1043-ISCHU |
| Authors |
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Marwa Gamal Elazab *1, Mamdouh Metwaly Elkady2, Mohamed Ahmed Abdelhakem2 1May University, Cairo, Egypt 2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| The aim of this paper is to use the second derivative of Chebyshev polynomials (SDCHPs) as new basis functions and present a highly efficient method for solving both linear and nonlinear boundary value problems (BVPs). Some important relations and properties for this new basis function have been introduced. Then, the operational matrix for the derivative was established by using SDCHPs. The established matrix via mixing between two spectral methods, collocation, and Galerkin, has been applied to solve BVPs. The basic idea is to convert ordinary differential equations into linear or nonlinear algebraic system with unknown coefficients, This system can be solved to get those coefficients. these coefficients can be determined and used to get the approximate solution. Consequently, an error analysis is investigated to ensure the convergence of the technique used. Finally, we solved some problems involving real-life applications and compared their solutions with exact and other solutions from different methods to verify the accuracy and efficiency of this method. |
| Keywords |
| Second derivative of Chebyshev polynomials, Spectral method, Pseudo-Galerkin, error analysis, Lane-Emden, fluid. |
| Status: Abstract Accepted (Poster Presentation) |