New numerical solutions of fractional-order Korteweg-de Vries equation - Inc, Mustafa; Parto-Haghighi, Mohammad; Akinlar, Mehmet Ali; Chu, Yu-Ming (ELSEVIER, 2020)
We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-discretization numerical scheme. Caputo type fractional-order derivative operators are used. We apply the method to some specific cases of the KdV equation. Computational results indicate that the method gives new and highly efficient solutions of the KdV equation.
Keywords: Time fractional Korteweg de Vries equation; Fictitious time integration; Group preserving scheme (GPS); Caputo derivative; GROUP PRESERVING SCHEME; KLEIN-GORDON EQUATIONS; GROUP SHOOTING METHOD; DIFFUSION; MODELS; Materials Science; Physics