In this paper, based on the modified block-by-block method, we propose a higher-order numerical scheme for two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy. This approach involves discretizing domain into large number of subdomains and using biquadratic Lagrangian interpolation each subdomain. The convergence high-order is rigorously established. We prove t...

Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.