What it solves

Equations: Faraday's law

\frac{\partial A}{\partial t} = - \frac{\nabla \times ( \nabla \times A + B _{0} )}{n} \times (\nabla \times A + B_{0}) - \frac{\int ( A - p f d p )}{n} \times (\nabla \times A + B_{0}), n = \int f d p .

Mid-point rule:

[M_{1} - \frac{Δ t}{2} F (n^_{h}^{0}, a^{n + \frac{1}{2}}) M_{1}^{- 1} (P_{1}^{⊤} W P_{1} + C^{⊤} M_{2} C)] a^{n + 1} = M_{1} a^{n} + \frac{Δ t}{2} F (n^_{h}^{0}, a^{n + \frac{1}{2}}) M_{1}^{- 1} (P_{1}^{⊤} W P_{1} + C^{⊤} M_{2} C) a^{n + 1} - Δ t F (n^_{h}^{0}, a^{n + \frac{1}{2}}) M_{1}^{- 1} P_{1}^{⊤} W P^{n} + Δ t F (n^_{h}^{0}, a^{n + \frac{1}{2}}) M_{1}^{- 1} C^{⊤} M_{2} b_{0} F_{ij} = - \int \frac{1}{n ^ _{h}^{0} g} G (\nabla \times A + B_{0}) \cdot (Λ_{i}^{1} \times Λ_{j}^{1}) d η .

FaradayExtended