Question

for dy/dx=-50y with y(o)=1
how can i find the condition for stability of the solution and how to solve it in euler explicit method

Answer 1

I know Euler, Euler midpoint and Euler trapezoidal, I assume u mean the first one....

Answer 2

is it just a differential equation or something more?

Answer 3

U have not specified an interval, so try with (0,1) , do the iteration with step h and examine what happens to the error (u want it to diminish).

Answer 4

oh, numerical method

Answer 5

Yes,

Answer 6

yes, initial value problem

Answer 7

For some reason I was thinking this
e^ i theta = cos theta + i sin thetha

Answer 8

Actually, this quite hard to explain on here....

Answer 9

Basically, u have to do a bit of algebra to determine an interval where the function is well conditioned...

Answer 10

Yes, I agree a lot of steps with the method, Runges Kutta stuffs

Answer 11

Usually, u don't have to worry about it too much, let the computer sort it out..

Answer 12

yep

Answer 13

Sometimes, u might have to intervene if it's a funny function....

Answer 14

But with euler method , we don't actually get function(traditional y=) but set of numbers which may be able to fit, right?

Answer 15

Well, u do

Y_r+1 = Y_r +h f(x_r,Yr) to see what interval will act to diminish the error in Y_r

Answer 16

Based on that, u can determine a step size.