); then solving the finite difference equation above,
= 
+ Δt [f(
) ]. So, 
= 
+ Δt (f(
) + f'(
)dy)
= 
+ Δt (f(
) + f'(
)(
- 
) )
= 
- Δt [f(
) - f'(
)
])/(1 - Δt f'(
) )
Finite Differencing Methods (Method 2): Implicit Forward Differences
Approximate f(y) with f(); then solving the finite difference equation above,= + Δt [f() ]. So, = + Δt (f() + f'()dy)
= + Δt (f() + f'()( - ) ) = - Δt [f() - f'()])/(1 - Δt f'() )
We define a function, PlotM2, which takes arguments Δt and InitialCondition and then uses ListPlot with Blue lines and Gray points.
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