Guys, i wanna understand this problem , i don't know how to do this. Please guide me.
Given the initial value problem: dy/dx = y, y(0)=1. Do the following.
1. Solve the initial value problem and show that e = y(1).
2. Apply Euler's method with h = 0.25 to approximate e =y(1).
3. Apply Improved Euler's method with h = 0.5 to approximate e = y(1).
4. Apply Runge-Kutta method with h = 1 to approximate e = y(1).
5. Find the errors of the above approximations of e. Which approximation is the best?
This is probably one of the easiest DEs to solve
you are given therefore
and this means
to show
The rest of these questions 2,3 & 4 involve different numerical schemes. Q5 is asking which one is the most accurate compared with your answer to Q1 of .
That is the point of letting him/her solve it himself, if being told it is of variables separable type s/he can't continue it is better that s/he tells us so we can diagnose the problem rather than provide a sample which s/he might think s/he understands but has only skimmed.
CB
Fair call CB, point taken
although after reading the question I went on the assumption that the poster is doing a course in numericals solutions to DEs. Therefore my solution to part 1 would have only been consequential and assumed knowledge for such a course. If anything I was hoping my assitance would've only acted as a reminder.