Applications of Sine–Cosine wavelets method for solving the generalized Hirota–Satsuma coupled KdV equation

In this article, we use the Sine–Cosine wavelets (SCWs) method to numerically solve the generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system. For this purpose, we use an approximation of functions with the help of SCWs, and we approximate spatial derivatives using this method. In this regard, to linearize the nonlinear terms of the equations, we use the quasilinearization technique. Also, the convergence analysis and the error estimation of the method are investigated. The operational matrix based on SCWs has a large number of zero components, which ensures good system performance and provides acceptable accuracy even with fewer collocation points. In the end, to show the efficiency and accuracy of the method in solving this system, a numerical example is provided and the results are compared with the Legendre wavelet (LW) method.