
Re: discretizing laplacian
Posted:
Feb 26, 2013 8:59 AM


Sandeep Kumar <searchsandy1712@gmail.com> writes: >Can anybody please tell me how to discretize Laplacian. I have  >laplacian(Un^2.Un+1), which is laplacian of product of Un^2 and Un+1. >where Un is U(j,n) and Un+1 is U(j,n+1). > > Thanks in advance. >Regards this makes no sense for me: with U already discretized, what should laplacian of this mean? If I remember right you one had laplacian(u^3) plus CrankNicholson, that means you need 1/2*(laplacian(u(x,t_n)^3)+laplacian(u(x,t_{n+1})^3)) where of course laplacian is w.r.t x and fortunately x is onedimensional. method 1: (d/dx)^2(u(x,t_n)^3)(x=x_i) = 3u(i,n)^2(u(i+1,n)2u(i,n)+u(i1,n))/h^2 +(6/h^2)(u(i+1,n)u(i1,n))^2 method2: (d/dx)^2(u(x,t_n)^3) = (1/h)^2 ( ((u(i+1,n)^2+u(i,n)^2)/2)*(u(i+1,n)u(i,n))  ((u(i,n)^2+u(i1,n)^2)/2)*(u(i,n)u(i1,n)) )
hth peter

