Undo finite difference with arbitrary timesteps

1. How can finite-difference method be improved?
2. Why use FDTD?
3. What are the disadvantages of finite-difference method?
4. What is the formula for finite-difference method?

How can finite-difference method be improved?

If you want to increase the accuracy of a finite difference scheme, you can always try increasing the degree of your stencil. On equidistant points, though, this can lead to numerical instabilities. To avoid these problems and still get high accuracy, I would suggest using Spectral Methods.

Why use FDTD?

The Finite-Difference Time-Domain (FDTD) method is a rigorous and powerful tool for modeling nano-scale optical devices. FDTD solves Maxwell's equations directly without any physical approximation, and the maximum problem size is limited only by the extent of the computing power available.

What are the disadvantages of finite-difference method?

With the finite-difference method, you may easily run into problems handling curved boundaries for the purpose of defining the boundary conditions. Boundary conditions are needed to truncate the computational domain.

What is the formula for finite-difference method?

Backward finite difference formula is(3.109)f′(a)≈f(a)−f(a−h)h.