Jacobi spectral discretization for nonlinear fractional generalized seventh-order KdV equations with convergence analysis

R. M. Hafez, Y. H. Youssri

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. 

Tbilisi Mathematical Journal, Vol. 13(2) (2020), pp. 129-148