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

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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.

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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,

 

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