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On the impact of boundary conditions in a wave equation
Contents
Mathematical model and solution method
The wave equation problem
Initial conditions
Boundary conditions
Numerical solution method
Demonstrations
Dirichlet and Neumann conditions: reflecting and mirroring boundaries
Effect of impulsive start of waves
Feeding of waves from the boundary
Open and periodic boundary conditions
Appendix: Numerical solution method
Approximating the wave equation
Approximating the initial conditions
Approximation of boundary conditions
Appendix: Computer code
Table of contents
Mathematical model and solution method
The wave equation problem
Initial conditions
Boundary conditions
Fixed \( u \)
Reflecting condition
Feeding a wave from the boundary
Open boundary condition
Periodic boundary condition
Numerical solution method
Demonstrations
Dirichlet and Neumann conditions: reflecting and mirroring boundaries
Numerical noise
Effect of impulsive start of waves
Feeding of waves from the boundary
Open and periodic boundary conditions
Error in the open boundary condition
Appendix: Numerical solution method
Approximating the wave equation
Approximating the initial conditions
Approximation of boundary conditions
Dirichlet conditions
Neumann conditions
Open boundary conditions
Periodic conditions
Appendix: Computer code
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