CENTRAL STENCIL FOR WENO 4th ORDER SCHEMES

Alberto

Hi to everybody. I'm writing a monodimensional code for solving shallow water equation with a WENO-based scheme. Do you know how to get the four coefficient of the third order polinomy ax^3+bx^2+cx+d for the central stencil? I mean: for the central stentil I think you use the cells i,i-1,i-2,i+1,i+2, so you have 5 equation and 4 unknown coefficient. Maybe is good to solve it with the least square method and the get the coefficients in this way?For the other stencil is straightforward because I have always 4 cells and so 4 coefficient and 4 equations. nobody have experience with that?is it correct this procedure? thanks a lot Alberto