an unconditionally stable spectral-finite difference scheme for the nonlinear time-fractional klein-gordon-zakharov system

This study presents an innovative numerical scheme to address the non-linear time-fractional coupled klein-gordon-zakharov equation‎. ‎the spatial derivatives are approximated using a pseudo-spectral method‎, ‎which utilizes lagrange polynomials at chebyshev points as basis functions‎. ‎time discretization is accomplished through the finite difference method‎. ‎the proposed scheme is rigorously proven to be unconditionally stable‎, ‎ensuring robustness in numerical simulations‎. ‎furthermore‎, ‎the time convergence order of the scheme is derived‎, ‎highlighting its reliability‎. ‎numerical experiments demonstrate the exceptional accuracy and robustness of the method‎, ‎with its exponential precision offering precise and reliable solutions‎. ‎this approach serves as a powerful tool for solving complex non-linear partial differential equations‎, ‎making it highly applicable in various scientific and engineering domains that demand effective and efficient computational techniques‎.