Abstract
In this work, we investigate the solitary wave solution of nonlinear Benjamin–Bona–Mahony–Burgers (BBMB) equation using a high-order linear finite difference scheme. We prove that this scheme is stable and convergent with the order of \(O(\tau ^2+h^4)\). Furthermore, we discuss the existence and uniqueness of numerical solutions. Numerical results obtained from propagation of a single solitary and interaction of two and three solitary waves confirm the efficiency and high accuracy of proposed method.
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