Wigglewave uses a finite difference method to solve the linearized governing equations for a torsion Alfvèn wave propagating in a plasma with negligible plasma beta and in a force-free axisymmetric magnetic field with no azimuthal component embedded in a high density divergent tube structure. Wigglewave is fourth order in time and space using a fourth-order central difference scheme for calculating spatial derivatives and a fourth-order Runge-Kutta (RK4) scheme for updating at each timestep. The solutions calculated are the perturbations to the velocity, v and to the magnetic field, b. All variables are calculated over a uniform grid in radius r and height z.