Wave equation 1d fortran software

Understand the basic concept of the finite element method applied to the 1d acoustic wave equation. Fdtd3ca fortran program to model multicomponent seismic. Solving the 1d wave equation step 3 write the discrete equations for all nodes in a matrix. Since we need to estimate the spatial derivatives only in the x 3direction, we apply a 1d stencil to locate wavefield variables and material parameters in space. I want to compare my numerical results with analytical solution. Step 3 write the discrete equations for all nodes in a matrix format and solve the system. To solve the 3d viscoelastodynamic equation in the plane wave domain, we apply a staggeredgrid fdtd with secondorder accuracy in time and fourthorder accuracy in space o2,4 e. Where can i get analytical solutions of an elastic wave. A fortran computer program for modeling full waveform propagation through a layered homogeneous onedimensional medium is presented.

Cython is an extension of python that offers the easiest way. Solving the 1d wave equation a threelevel scheme in time. This can quite easily be done by adding a little extra code to our program. I am trying to solve the 1d heat equation using cranknicolson scheme. This paper introduces the fourth order compact finite difference method for solving the numerical solution of onedimensional wave equations. And for that i have used the thomas algorithm in the subroutine. Numerical methods for solving the heat equation, the wave. I am solving velocity stress formulation of elastic wave equation. Finite difference methods for 2d and 3d wave equations a natural next step is to consider extensions of the methods for various variants of the onedimensional wave equation to twodimensional 2d and threedimensional 3d versions of the wave equation. Where can i get analytical solutions of an elastic wave equation. Pdf fourth order compact finite difference method for. The wave equations may also be used to simulate large destructive waves waves in fjords, lakes, or the ocean, generated by slides earthquakes subsea volcanos meteorittes human activity, like nuclear detonations, or slides generated by oil drilling, may also generate tsunamis propagation over large distances wave amplitude increases near.