Solving the 1D Helmholtz Differential Equation Using Finite Differences

This Demonstration implements a recently published algorithm of an improved finite difference scheme for solving the Helmholtz differential equation

-

U

xx

-

2

k

U=f(x)

in one dimension. Dirichlet and Sommerfeld boundary conditions are supported. Different source functions

f(x)

can be specified. Sommerfeld boundary conditions can be specified at either end of the domain but not at both ends at the same time. The current value of points per wavelength (PPW) is shown at the top of the display. You can also vary the

k

value. You can view the matrix

A

and its eigenvalues using the dropdown menu in the top row.