- #1

- 10

- 0

## Main Question or Discussion Point

Hi

Im a bit stuck on the method for Euler Integration. I have the following first order differential equation:

dx/dt = (x-at) / (x / a+t)

where constant a = 1.0V/s, and initial condition x = 1.0V at t=0s

I have a time step of 0.02 and I need to calculate the output voltage at a time t = 0.2s

So I have the Euler Integration formula: x(t + ^t) = x(t) + ^t.f(x,t)

and I've started putting the values into an Excel spreadsheet, with columns as follows:

t | x(t) | f(x,t) | ^x = ^t.f(x,t)

I have values for all the first row for these columns but an example in a textbook has an additional column called x(exact) which appears to calculate an error value? I am not sure how to calculate this value, and am also unsure about how to move on with the iteration? What values should I move down for further rows?

I have searched the web but can't find any sites I can make sense of - can anybody help me? I hope my question makes sense...

Thanks

Jimbo :)

Im a bit stuck on the method for Euler Integration. I have the following first order differential equation:

dx/dt = (x-at) / (x / a+t)

where constant a = 1.0V/s, and initial condition x = 1.0V at t=0s

I have a time step of 0.02 and I need to calculate the output voltage at a time t = 0.2s

So I have the Euler Integration formula: x(t + ^t) = x(t) + ^t.f(x,t)

and I've started putting the values into an Excel spreadsheet, with columns as follows:

t | x(t) | f(x,t) | ^x = ^t.f(x,t)

I have values for all the first row for these columns but an example in a textbook has an additional column called x(exact) which appears to calculate an error value? I am not sure how to calculate this value, and am also unsure about how to move on with the iteration? What values should I move down for further rows?

I have searched the web but can't find any sites I can make sense of - can anybody help me? I hope my question makes sense...

Thanks

Jimbo :)