A new algorithm for analysis and simulation of (2+1) Korteweg–de Vries–Rosenau-regularized long-wave model

This paper designs a new algorithm based on scale-3 Haar wavelets to emulate the nonlinear (2+1) Korteweg–de Vries–Rosenau-regularized long-wave model. For the flourish of the algorithm, the primary effort is semi-discretization in temporal variable via finite difference schemes, namely forward and Crank–Nicolson differences, and then truncation error is discussed. After that, full discretization is made via scale-3 Haar wavelets. In the end, the convergence analysis of the scale-3 wavelets is discussed. To check the competence and exactitude of the scheme and to predict the nature of the wave behaviors, one- and two-dimensional numerical problems are taken into account.