Numerical and analytical investigations for solution of fractional Gilson–Pickering equation arising in plasma physics

Abstract

This paper deals with the numerical solution of the time-fractional Gilson–Pickering equation using the Kansa method, in which the multiquadrics were utilized as the radial basis function. To achieve this, a meshless numerical scheme based on the finite difference along with the Kansa method has been presented. First, the finite difference approach has been utilized to discretize the temporal derivative, and subsequently, the Kansa method is employed to discretize the spatial derivatives. The stability and convergence analysis of the numerical scheme are also elucidated in this paper. Furthermore, the soliton solutions have been acquired by implementing the Kudryashov method for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.