Modified Homotopy Perturbation Method for Solving Benjamin- Bona- Mahony-Burger Equation

The Benjamin–Bona–Mahony–Burgers (BBMB) equation is an important nonlinear partial differential equation in fluid mechanics, used to describe the propagation of long waves. Due to its nonlinearity, obtaining exact solutions is difficult, which motivates the use of efficient approximate methods.In this paper, the BBMB equation is solved using the Variational–Homotopy Perturbation Method (VHPM), which combines the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM), providing a rapidly convergent series solution without requiring a small perturbation parameter. The results obtained by VHPM are compared with those of VIM and HPM. The solution is expressed as a series and truncated at the second-order term due to the method’s fast convergence. Numerical examples are presented for both homogeneous and non-homogeneous cases, and the accuracy is evaluated using the error norms L_2 and L_∞.The results show that VHPM produces more accurate and stable solutions than the other methods. The reported error norms and graphical comparisons confirm the effectiveness and reliability of the proposed technique. Consequently, the VHPM is shown to be a powerful and efficient tool for solving the BBMB equation and similar nonlinear partial differential equations. Keywords: Benjamin, Bona, Mahony, Berger’s Equation, Variational, Homotopy Perturbation Method.