Solved: Use the Forward-Difference method to approximate the solution to the following
Chapter 12, Problem 12.2.6(choose chapter or problem)
Use the Forward-Difference method to approximate the solution to the following parabolic partial differential equations. a. u t 4 2 2u x 2 = 0, 0 < x < 4, 0 < t; u(0, t) = u(4, t) = 0, 0 < t, u(x, 0) = sin(x/4)(1 + 2 cos(x/4)), 0 x 4. Use h = 0.2 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et sin(x/2) + et/4 sin(x/4). b. u t 1 2 2u x 2 = 0, 0 < x < 1, 0 < t; u(0, t) = u(1, t) = 0, 0 < t, u(x, 0) = cos x 1 2 , 0 x 1. Use h = 0.1 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et cos (x 1 2 ).
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer