wave_pde

wave_pde, an Octave code which uses finite differences in space, and the method of lines in time, to set up and solve the partial differential equations (PDE) known as the wave equations, utt = c uxx, in one spatial dimension and time.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

wave_pde is available in a MATLAB version and an Octave version.

Related Data and codes:

wave_pde_test

advection_pde, an Octave code which solves the advection PDE dudt + c * dudx = 0 in one spatial dimension, with a constant velocity c, and periodic boundary conditions, using the FTCS method, forward time difference, centered space difference.

allen_cahn_pde, an Octave code which sets up and solves the Allen-Cahn reaction-diffusion system of partial differential equations (PDE) in 1 space dimension and time.

artery_pde, an Octave code which solves a partial differential equation (PDE) that models the displacement of arterial walls under pressure.

diffusion_pde, an Octave code which solves the diffusion partial differential equation (PDE) dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using FTCS, the forward time difference, centered space difference method.

gray_scott_pde, an Octave code which solves the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, displaying a sequence of solutions as time progresses.

schroedinger_linear_pde, an Octave code which solves the complex partial differential equation (PDE) known as Schroedinger's linear equation: dudt = i uxx, in one spatial dimension, with Neumann boundary conditions.

schroedinger_nonlinear_pde, an Octave code which solves the complex partial differential equation (PDE) known as Schroedinger's nonlinear equation: dudt = i uxx + gamma * |u|^2 u, in one spatial dimension, with Neumann boundary conditions.

spiral_pde, an Octave code which solves a pair of reaction-diffusion partial differential equations (PDE) over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals.

string_pde, an Octave code which sets up and solves the partial differential equations (PDE) describing a vibrating string.

tumor_pde, an Octave code which solves the tumor angiogenesis partial differential equations (PDE) using MATLAB's pdepe() function.

Source Code:

• dbydx_pp.m, estimates spatial derivative when both boundaries are periodic.
• integral_pp.m, estimates the integral of a quantity over an interval, whose values are given at equally spaced points, and for which a periodic boundary condition applies.
• laplacian_pp.m, estimates the laplacian of a quantity over an interval, whose values are given at equally spaced points, and for which a periodic boundary condition applies.
• wave_conserved.m, evaluates the energy of a solution of the wave PDE.
• wave_deriv.m, returns the right hand side of the wave PDE.
• wave_exact.m, evaluates the exact solution of the wave PDE.
• wave_exact_xx.m, evaluates the exact second spatial derivative of U.
• wave_init.m, evaluates the initial condition of the wave PDE.
• wave_parameters.m, returns the parameters of the wave PDE.