A modied Runge–Kutta scheme for the generalized Benjamin–Bona–Mahony–Burgers' equation

This paper presents a modified Runge–Kutta (MRK) scheme for the generalized Benjamin–Bona–Mahony–Burgers equation. The MRK method separate this equation into two parts which apply different finite difference scheme in space, and finally use fourth-order Runge–Kutta method in time.The scheme is conditionally stable and convergent with order of $O(\tau^4+h^2)$, the Comparisons of the existing numerical methods demonstrate that this scheme is capable of high accuracy and stability.