| Autor: |
Jan, Hameed Ullah, Shah, Irshad Ali, Tamheeda, Ullah, Naseeb, Ullah, Arif |
| Předmět: |
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| Zdroj: |
Punjab University Journal of Mathematics; 2023, Vol. 55 Issue 9/10, p357-370, 14p |
| Abstrakt: |
Partial differential equations (PDEs) describe simulation of physical phenomena occurring in different fields of science and engineering. The analysis of solutions of nonlinear wave equations have been gaining a lot of popularity in the last two decades. Such wave equations have many applications in applied mathematics and theoretical physics. The importance of PDEs that explain nonlinear waves defined by Sine-Gordon (SG) equation are crucial. The SG equation is a particular instance of the Klein-Gordon (KG) equation, which is crucial in a number of scientific fields, such as solid state physics, nonlinear optics, and quantum field theory. This equation is also a description of a soliton wave that exists in many physical situations. Different analytical as well as numerical techniques were used to develop the exact and approximate solution of SG equation. In this article, we explore the numerical solution of the one-dimensional nonlinear SG problem using RBF-FD approach. The scheme is a combination of radial basis functions (RBFs) with finite differences (FD) for constructing local spatial approximations to SG equation. For execution of time variable in the given model equation, Runge-Kutta (RK) time steeping approach is utilized. To verify the validity of our method, solutions to some test problems are examined. Accuracy of the proposed scheme is verified through L1, L2, "RMS" and "MAE" error norms. The solutions acquired by suggested RBF-FD approach are also compared to earlier work and the obtained results are batter and in good agreement with the exact solution. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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