finite difference method evaluation

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Soumyadeep
Soumyadeep on 11 Aug 2022
Answered: Torsten on 11 Aug 2022
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?

Answers (1)

Torsten
Torsten on 11 Aug 2022
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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