An effective comparison with Least Square method for solving fractional gas dynamic equations. | ||||
| Frontiers in Scientific Research and Technology | ||||
| Volume 7, Issue 1, December 2023 PDF (785.19 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/fsrt.2023.233651.1104 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Ahmed Hassan Kamal  1; A. A. M. Arafa2; S. Z. Rida3; M. A. Dagher4; Hamed El-Sherbiny5
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| 1Faculty of Petroleum and Mining Engineering, Suez University, Suez, Egypt | ||||
| 2Department of Mathematics, College of Science and Arts, Qassim University, Al Mithnab, Saudi Arabia, Department of Mathematics, Faculty of Science, Port Science University, Port Said, Egypt | ||||
| 3Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt | ||||
| 4Department of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez University, Suez, Egypt | ||||
| 5Mathematics and Computer Science Department, Faculty of Science, Suez University | ||||
| Abstract | ||||
| Nonlinear time-fractional partial differential equations, especially nonlinear time-fractional Gas dynamic equations, can be resolved by applying the Optimal Homotopy Asymptotic Method (OHAM) and the Least Square Residual Power Series Method (LSRPSM). A Fractional-order derivative that has numerical values in the closed interval [0, 1] is being employed in the Caputo meaning. These approaches are compared based on their computing complexity, convergence rate, and approximation error. The present study demonstrates that when these techniques are assigned to nonlinear differential equations of fractional order, they exhibit differing convergence rates and approximation errors. Using the Matlab software, perform numerical computations and graphics for fractional gas differential equations. The results of this comparison are compared to the exact solution to demonstrate how much more efficient and precise our methods are at solving nonlinear differential equations. In comparison to (OHAM), the research's findings demonstrate the validity and efficiency of the series solution utilizing (LSRPSM), showing the importance of these methods in the study of fractional differential equations. | ||||
| Keywords | ||||
| Least square residual power series method; optimal homotopy asymptotic method; fractional nonlinear gas dynamics equation; Caputo’s fractional derivative | ||||
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