finite difference method evaluation

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Soumyadeep
Soumyadeep 2022-8-11
回答： Torsten 2022-8-11
I have an equation of the form: [F(i+1)-F(i)]/[t(i+1)-t(i)] = A* [E(i+1)-E(i)] + B* [F(i+1)-F(i)]
A, B = constants
Here F and E are dependent on t. With increment of t with dt=0.001, for i=0, F(0)=0, E(0)=0.
At t=t+dt = 0.000001,
t (max)= 1
t (min)= 0
F(1) / t(1) = A * E(1) + B* F(1)
From t=t+2dt = 0.000002, F(2) -F(1) / t(2) - t(1) = A * [E(2)- E(1)] + B * [F(2) - F(1)] ......... and so on
Continues till t=1
Can anyone suggest comment for solving this equation?

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回答（1 个）

Torsten
Torsten 2022-8-11
As you can see from the two equations you wrote down, each equation gives two new unknowns.
Thus in the end, you have N equations for (2*N) unknowns which means that your linear system of equations is drastically underdetermined. E.g. E = F = 0 for all times is a solution.
As long as you cannot give a second recursion or fix E or F for all times, a reasonable solution is out of reach.

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