Numerical methods for PDE (two quick examples) Discretization ...
www.public.asu.edu › pde_slides_numericalNumerical methods for PDE (two quick examples) Discretization: From ODE to PDE For an ODE for u(x) defined on the interval, x ∈ [a, b], and consider a uniform grid with ∆x = (b−a)/N, discretization of x, u, and the derivative(s) of u leads to N equations for ui, i = 0, 1, 2, ..., N, where ui ≡ u(i∆x) and xi ≡ i∆x. (See ...