Multi-domain reproducing kernel finite difference method for Burgers equation

A multi-domain reproducing kernel finite difference method is presented for Burgers equation. It is a domain decomposition method, which combines reproducing kernel finite difference method with penalty method. Firstly, we decompose the global computational domain into a number of subdomains, hence the equation can be solved in subdomains instead of the whole domain. Then, we apply reproducing kernel finite difference method for space discretion, a fourth order Runge-Kutta scheme for time discretion in each subdomain. Finally, we apply penalty method for dealing with the inner boundary condition, so that each subdomain with inner boundary condition can be solved as a whole while not considering it independently. Numerical examples are given to test the efficiency of the represented method.