A Novel Scheme for Numerical Analysis of Fractional Order Coupled System of Partial Differential Equations (Contemporary Mathematics, 2025)
This work focused on developing and analyzing semi analytical scheme that is a computer-based approach for solving complex evolutionary partial differential equations (PDEs) of the Burger type. A novel scheme named Asymptotic Homotopy Perturbation Transform Method (AHPTM) is introduced for solving fractional order coupled nonlinear Burgers PDEs. The Caputo fractional form has been considered for derivatives. Nonlinear Burgers PDEs have various applications in fluid dynamics, traffic flow, nonlinear acoustics and signal processing. The algorithm of AHPTM is a fast convergent approach that has been developed by combining the Laplace transformation and the asymptotic homotopy perturbation method. Using the technique of AHPTM, three test problems of one-dimensional coupled nonlinear Burgers PDEs have been solved. This work demonstrates the smooth and easy implementation of solving problems by using MATLAB programming. The numerical results demonstrate that this novel approach is simple, easy and computationally capable for the problems. An error estimate is also required to solve the problem. To demonstrate the effectiveness and accuracy of the said solver, the solutions to the problems are tabulated and graphically displayed via using MATLAB software.
Keywords: asymptotic homotopy method; numerical analysis; caputo derivative; burgers equation