Direct numerical methods for solving a class of third-order partial differential equations

In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a flat plate. An efficient numerical method is proposed for PDE of type I. The PDE of type I is converted to a system of third-order ordinary differential equations (ODEs) using the method of lines. The system of ODEs is then solved using direct Runge–Kutta which we derived purposely for solving special third-order ODEs of the form y‴=f(x,y). Simulation results showed that the proposed RKD-based method is more accurate than the existing finite difference method.