We developed a numerical scheme to solve the nonlinear fractional (NF) generalized seventh order KdV (sKdV) equation with time-space-fractional using the shifted Jacobi collocation method. Basically, a time-space collocation approximation for temporal and spatial discretizations is employed efficiently to tackle these equations. The convergence and stability analyses of the suggested basis functions are presented in-depth. The validity and efficiency of the proposed method are investigated and verified through numerical examples.
The authors would like to thank the handling editor for his effort in the proof reading of the paper and also for his constructive and valuable comments which have improved the paper.
"Jacobi spectral discretization for nonlinear fractional generalized seventh-order KdV equations with convergence analysis." Tbilisi Math. J. 13 (2) 129 - 148, April 2020. https://doi.org/10.32513/tbilisi/1593223223