# Questions tagged [finite-difference-methods]

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### Discretization of second order nonlinear ODE using finite difference with pseudo-spectral method

I have the following equation that was discretized using pseudo-spectral method in 2D with periodic BCs that works. $$\nabla_{\perp} \cdot \left( n \nabla_{\perp} \psi \right) = \textbf{S}$$ ...
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### Determining if a difference operator is of positive type

My question is about c. As per the definition, a difference operator $L_hU_m:=-a_mU_{m-1}+b_mU_m-c_mU_{m+1}$ is positive type if $a_m\geq0$, $c_m\geq0,$ $b_m\geq a_m+c_m$, and $b_m>0$. Application ...
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### Clarification on Difference Formula for nodes near boundary

The above is an extract from my precis on numerical solutions to PDE, finite difference method giving explanation for difference formula for nodes near boundary when step length is not equal (...
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