The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation

This paper develops a method for the numerical solution of the nonlinear regularized long wave equation. This method discretizes the unknown solution in two main schemes. The time discretization is accomplished by means of an implicit method based on the $$\theta $$ -weighted and finite difference methods, while the spatial discretization is described with the help of the finite difference scheme derived from the local radial basis function method. The advantage of the local collocation method is based only the discretization nodes located in each sub-domain, requiring to be considered when obtaining the approximate solution at every node. It also tackles the ill-conditioning problem derived from global collocation method. Besides, the stability analysis of the proposed method is analyzed and the accuracy of it is examined with $$L_{\infty }$$ and $$L_2$$ norm errors. At the end, the results obtained by the proposed method are compared with the methods given in previous works and it indicates an improvement in comparison with previous works.