Boundary Value Problems/Lesson 6

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1D Wave EquationEdit

Derivation of the wave equation using string model.

General form for boundary conditions.Edit

Wave equation with Dirichlet Homogeneous Boundary conditions.Edit



In the homogeneous problem with ,

Finding a solution: u(x,t)Edit

Let
then substitute this into the PDE.


Where is a constant that can be positive, zero or negative. We need to check each case for a solution.

Wave Equation with nonhomogeneous Dirichlet Boundary ConditionsEdit

In the homogeneous problem  
 
 

Wave Equation with resistive dampingEdit

In the homogeneous problem