CrankNicolson Order Let the function y(x, ) solve the equation y = yxx and be sufficiently smooth. With the difference quotient xxwi, := wi+1,

Crank–Nicolson Order Let the function y(x, τ) solve the equation yτ = yxx and be sufficiently smooth. With the difference quotient δxxwi,ν := wi+1,ν − 2wi,ν + wi−1,ν Δx2 the local discretization error  of the Crank–Nicolson method is defined  := yi,ν+1 − yi,ν Δτ − 1 2 (δxxyi,ν + δxxyi,ν+1) . Show  = O(Δτ 2) + O(Δx2).