ABSTRACT
This chapter presents the Petrov–Galerkin method for the numerical solution of the fractional Korteweg–de Vries–Burgers (KdVB) equation and fractional Sharma–Tasso–Olver (STO) equation. It establishes the efficiency and accuracy of the Petrov–Galerkin method in solving fractional differential equations numerically by implementing a linear hat function as the trial function and a quintic B-spline function as the test function. The chapter considers one of the well-known equations, namely, the KdVB, which plays an essential role in both applied mathematics and physics. Especially KdV type equations have been paid more attention due to their various applications in plasma physics, solid-state physics, and quantum field theory. With the aid of conducting a comparison between the absolute error for the obtained numerical results and the analytic solution of the KdVB equation, the chapter analyses the accuracy of the proposed procedure.
