Approximate solution to nonlinear system of equation: Pourreza transform variational iteration method

सार

Novel mathematical methods were established to investigate the numerical results of a coupled Burger’s equation (CBE) and a shallow water- coupled system of fractional order with Caputo, Caputo Fabrizio (CF), and Atangana Baleanu Caputo (ABC) derivatives under initial conditions. The method was obtained by coupling the Pourreza transform with the variational iteration method. The stability analysis of PVIMABC was conducted to show the effectiveness of the scheme, and the comparison of the numerical results of PVIMC , PVIMCF , and PVIMABC with existing methods was presented to show the validity and accuracy of this proposed numerical technique. The 3D graphical results were used to compare the exact and the approximate solution at the classical order of the illustrated examples, and 2D graphical results are obtained to show the numerical results of the illustrated examples at different fractional orders. Also, the tables obtained show the reliability and the convergence of the proposed method. For calculations, the Maple software package was utilized.