Solution Found!
Consider u t = k 2u x2 subject to u(0, t)=0, u x (L, t) = hu(L, t), and u(x, 0) = f(x)
Chapter 5, Problem 5.8.1(choose chapter or problem)
QUESTION:
Consider u t = k 2u x2 subject to u(0, t)=0, u x (L, t) = hu(L, t), and u(x, 0) = f(x). (a) Solve if hL > 1. (b) Solve if hL = 1.
Questions & Answers
QUESTION:
Consider u t = k 2u x2 subject to u(0, t)=0, u x (L, t) = hu(L, t), and u(x, 0) = f(x). (a) Solve if hL > 1. (b) Solve if hL = 1.
ANSWER:Step 1 of 9
The partial differential equation is given as,
The initial condition is given as,
Substitute , and also divide the differential equation by , so that its gets converted to a time-dependent ordinary differential equation (ODE) as follows,
The corresponding solution is,