Solve by using D'Alembert's solution with the even extensions of f(x) and g(x)

where

, where

where

Printable View

- Feb 23rd 2009, 01:02 PMflamingPartial Differential Equation using D'Alembert's approach
Solve by using D'Alembert's solution with the even extensions of f(x) and g(x)

where

, where

where - Feb 23rd 2009, 02:55 PMThePerfectHacker
Since we have the boundary condition we would consider even extensions. Let be even extensions, and we will also assume that these extensions are well-behaved to satisfy the condition of D'Alembert's solution. Thus, we have that for . Thus, the solution is given by:

.

Notice that therefore , this is precisely what we want.