Backward Euler Method
Statement of the Problem
Solve the problem using the Rk4 algorithm.
Compare your answers to the exact
answers.
What do you suspect is the problem?
Recall that Rk4 is an explicit method.
Write a maple worksheet for performing the Backward Euler method calculation.
Use Newton’s method to solve for the solution at each time step.
Use three Newton
iterations per time step in your calculation.
Run the solver for each of there systems.
Compare it to the exact answer.
How
do you know that your solver is working correctly?
Why does this order method perform
better than the more accurate RK4?
Description of the Algorithm
Forward Euler, Backward Euler, what’s next!? Upside down Euler…maybe someday.
For now, lets just stick with Backward Euler.
The main difference between BE and FE is
that BE is implicit and FE is explicit. Now, you are probably wondering what the
difference between implicit and explicit.
The mathematical way of displaying follows:
Implicit(BE)
Y
n+1
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 Spring '09
 Couillette
 Math, ΔT, Numerical ordinary differential equations, Backward Euler, Stiff equation, Explicit and implicit methods

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