| Spectral Tau Explicit Form for Approximating Solutions to Real-Life IBVPs Using Chebyshev Derivatives |
| Paper ID : 1021-ISCH |
| Authors |
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Toqa Alaa-Eldeen *1, Mohamed A Abdelhakem2, Mamdouh Metwally Elkady3 1Assistant Lecturer of Mathematics - Basic Science - Faculty of Engineering - Canadian International Collage (CIC) 2Mathematics Department, Faculty of Science, Helwan University Helwan, Cairo, Egypt Canadian International College. 3Mathematics Department, Faculty of Science, Helwan University, Helwan 11795, Egypt |
| Abstract |
| This paper established a functional design of the spectral Tau method (STM) upon the first derivatives of Chebyshev polynomials (FDCHPs). A new linearization relation has been developed. Hence, this relation and another investigated one for integration have been used via the Tau method to execute the Tau integration analytically. Moreover, explicit algebraic systems for solving the Lane-Emden and Riccati equations and the contamination of a system of three artificial lakes are introduced. The convergence and error analysis are explored in depth. Some enlightening boundary value problems (BVPs) for real-life and physical applications, as singularly perturbed equations, are provided to guarantee that this approach is authentic, reliable, and appropriate. Accurate results are obtained using only a few numbers of retained nodes. The different outcomes, patterns, and better results showed that the FDCHPs differ from Chebyshev polynomials of the second kind Keywords: Chebyshev polynomials' derivative; Tau method; BVPs; Lane-Emden equation; Riccati equation; singularly perturbed equation; contamination model, three lakes model. |
| Keywords |
| Chebyshev polynomials' derivative; Tau method; BVPs; Lane-Emden equation; Riccati equation; singularly perturbed equation; contamination model, three lakes model. |
| Status: Abstract Accepted (Poster Presentation) |