| Monic Chebyshev’s First Derivative pseudo-Galerkin method for solving linear and non-linear IBVPs |
| Paper ID : 1041-ISCHU |
| Authors |
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Hager Alaa Elden Mahmoud *1, Mamdouh Metwaly Elkady2, Mohamed Ahmed Abdelhakem2 1Mathematics department, faculty of science, helwan university, Helwan, Cairo ,Egypt 2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| This paper has presented a monic of Chebyshev’s first derivative pseudo galerkin method (PG- MFDCHPs), a methodology that proposes accurate and efficient numerical formulas to solve linear and non-linear ordinary differential equations (ODEs) depending on the monic of Chebyshev’s first derivatives as new basis functions. Then, a new operational matrix of derivatives with any integer order of monic Chebyshev’s first derivative is presented. In addition, a new linearization relation has been proved. Consequently, this relation and other relations have been used via the pseudo-Galerkin method to convert the given initial boundary value problems (BVPs) to a system of algebraic equations. The error analysis is studied to verify the convergence of the proposed method. Finally, our obtained method is applied to several numerical applications and real-life problems, such as the Lane-Emden equation, Riccati equation, Bratu-type BVP, and higher-order BVP. The obtained results are compared with other results to ensure the efficiency and accuracy of the proposed method. |
| Keywords |
| monic of Chebyshev’s first derivative pseudo galerkin method (PG- MFDCHPs). ordinary differential equations (ODEs). boundary value problems (BVPs). |
| Status: Abstract Accepted (Poster Presentation) |