Question

Newtons method to solve partial differential equations

Answer 1

Explanation:

For solving nonlinear partial equations, say −Δy+f(y)=0, there are two common approaches:

Fixed point iteration: Pick y0 and for k=1,… solve −Δyk+1+f(yk)=0. (That is, you replace y by yk+1 in all linear terms and by yk in all nonlinear terms.)

Newton's method: Pick y0 and for k=1,… solve −Δδy+f′(yk)δy=−(Δyk+f(yk))