Piecewise exact solution of nonlinear momentum conservation equation with unconditional stability for time increment

Exact solution is adopted for computation of the inviscid Burgers equation on finite difference grid. Initial condition and following computed values of the independent variable are assumed to be piecewisely linear between fixed grid points, and local exact solution is used to find the value at the next time step at each grid point. Comparisons of Piecewise Exact Solution Method (PESM), existing upwind scheme, and the analytic solution show that the present method is more accurate than the upwind scheme. The unconditional stability is a strong merit of this method and is shown with a test result.