In this paper, we use the rational radial basis function (RRBF) method for solving the one dimensional Sine-Gordon (SG) equation, especially the case with steep front or sharp gradient solutions. The time and spatial derivatives are approximated by the finite difference and RRBF method, respectively. Some numerical experiments are given in both perturbed and unperturbed cases, and are compared with some other numerical methods to confirm the good accuracy of the presented method. The conservation law of energy is also investigated.
Shiralizadeh, M., Alipanah, A., & Mohammadi, M. (2022). Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions. Journal of Mathematical Modeling, 10(3), 387-405. doi: 10.22124/jmm.2021.20458.1780
MLA
Mansour Shiralizadeh; Amjad Alipanah; Maryam Mohammadi. "Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions". Journal of Mathematical Modeling, 10, 3, 2022, 387-405. doi: 10.22124/jmm.2021.20458.1780
HARVARD
Shiralizadeh, M., Alipanah, A., Mohammadi, M. (2022). 'Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions', Journal of Mathematical Modeling, 10(3), pp. 387-405. doi: 10.22124/jmm.2021.20458.1780
VANCOUVER
Shiralizadeh, M., Alipanah, A., Mohammadi, M. Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions. Journal of Mathematical Modeling, 2022; 10(3): 387-405. doi: 10.22124/jmm.2021.20458.1780
)