A modified reproducing kernel method for solving Burgers' equation arising from diffusive waves in fluid dynamics

As we known, reproducing kernel method (RKM) has been presented for solving differential equations for initial and boundary value problems. However, the direct application of the RKM presented in the previous works cannot produce good numerical results for Burgers' equation. To solve this problem, this paper give a modified reproducing kernel method by piecewise technique. The exact solution is given by reproducing kernel functions in a series expansion form, the approximation solution is expressed by n-term summation of reproducing kernel functions. The three numerical experiments results show that the piecewise method is more easily implemented and effective. Some numerical results are also compared with the results obtained by other methods.