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The Backward Euler method gives a system of algebraic equations

The Backward Euler scheme:

un+1=un+Δt(aun+1+bvn+1),vn+1=vn+Δt(cun+1+dvn+1). which is a 2×2 linear system:

(1Δta)un+1+bvn+1=un,cun+1+(1Δtd)vn+1=vn,

Crank-Nicolson also gives a 2×2 linear system.

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