I am wondering what the state-of-the-art regarding grid definition and construction, for solving PDEs using finite differences. I know some techniques are described in Duffy's Finite difference methods in financial engineering. I am aware of sparce grids and finite difference methods without boundary conditions.

However, my question or seek for advice is if someone knows some good references or techniques that are well-known to work, specially in the context of quantitative finance, i.e. give good results when applied to solve BS PDE equations (let it be SLV, a stock together with stochastic rates, etc).

I'd appreciate for example some references with discussions on how to set an upper/lower limit on the grid or how the spacing should be defined.

Thanks a lot!



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