# Questions tagged [eulers-method]

Euler's method is a numerical method to solve first-order first-degree differential equations with a given initial value.

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### Local vs global truncation error

I was reading about local and global truncation error, and, I must be honest, I'm not really getting the idea of the two and what's the difference. Lets focus on the forward Euler method in ...
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### A nice way to do Euler's method on a calculator?

As part of the calculator paper for IB (International Baccalaureate), we may be asked to do Euler's method, for say, 10 iterations. While it is feasible to do with a calculator (slightly easier if ...
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### Strange oscillations in Matlab

I have created a midpoint algorithm to solve 2nd order ODEs in Matlab. And now Im comparing my solver with built in - ode23s. I have used a harmonic motion described as a 2nd order ODE, the .m file ...
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### Compute approximation of ODE using one step of explicit/implicit Euler method

I'm given the IVP: $$u^{(3)}(t) + u'(t) = tu(t)$$ $$u''(2) = 2$$ $$u(2) = 0$$ $$u'(2) = 1$$ and am asked to approximate the solution for $t=2.5$ using one step of the explicit Euler-method and one ...
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### Euler's method.

So for my assignment I have to code a program to solve first order ODE's using Euler's Method. My program works, it returns the right values. (I checked using an online calculator). However, solution ...
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### What's the minimum step size that can be used in Euler's method before it becomes unreliable?

In particular, if Euler's method is implemented on a computer, what's the minimum step size that can be used before rounding errors cause the Euler approximations to become completely unreliable? I ...
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### Crank-Nicolson Scheme equivalent to a forward and backward Euler method

I am trying to show that, for the equation $$y'+\alpha y=0$$ alternating between a forward Euler method step for $y_{2n}$ and a backward Euler step for $y_{2n+1}$ with time-step $h$ is equivalent ...
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### Using Euler's relation to transform to cosine

input is $f_2(t) = Acos(w_0 t + \phi)$ output $y_2(t)$ is $\frac{A}{2} e^{j \phi} H(jw_0) e^{jw_0 t} + \frac{A}{2} e^{-j \phi} H(-jw_0) e^{jw_0 t}$ okay so I need the step in between, how were the ...
I have an exercise that I do not understand. We have to solve an initial value problem: $$\begin{array}{ccl} y'(t) &=& f(t,y(t)) \\ y(a) &=& y_0 \end{array}$$ We have to derive ...