Question

(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a function u(x, t) of two variables, consider the second order partial differ- ential equation CER This is the so-called snave equation. Construct a numerical method for approx imating solutions to this equation, by using the second forward difference for the variable t, and the second central difference for the variable z. Simplify your answer by writing the time-step, w uat),as a linear values ua.m where m<j of (c) Discuss some subtleties that might arise in your numerical method. [E&do you think this method produces a numerical solution that stays bounded for all time?)

Answer 1

レ1m 2 abive egh ah an w and sable ムや,人,2. うーヤぉ her er

(a 2