# 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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### Solving $y' = x+y$ with Euler's method

I was going over Euler's method for solving DE and I had an idea: Could we use it to get an exact solution to a DE by considering an infinitesimal step size? This is the main idea: if the ...
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### Will a linearized dynamical system be stabile when using it with Euler's Method?

Assume that we have a dynamical system $\dot x = f(x, u)$ and I want to simulate the system with Euler's Method. $$x = x + af(x, u)$$ Where $a$ is a small number. This can create unstability. What if ...
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### Adaptive step size for Euler Method - How to create?

I think Euler's Method is a great way to simulate ODE:s. It's not the most accurate, but it's the fastest and simplest. Euler's Method is usaly used with fixed step size, where ...
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### How can I apply the Euler–Maruyama approximation to the following SDE?

I'm trying to apply the Euler–Maruyama discretization to a python code using this Wikipedia page Wikipedia page where it says that the SDE $$dX_t = a(X_t, t) dt + b(X_t, t) dW_t, \quad X_0 = x_0$$ ...
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### Fundamental limit in the problem of energy of the Euler-Method for harmonic oscilations

I was discussing with one friend and he sent me a strange manipulation. It's a common result that the Euler Method isn't good for Harmonic oscillations because the energy isn't conserved. ...
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### Combining Multistep and Truncated Taylor methods

Consider solving an ODE $d_t x = f(x, t)$ numerically. The 1st-order Truncated Taylor method is simply Euler's method: $x_{n+1} = x_n + h_n f(x_n, t_n)$. We can "improve" Euler's method ...
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### Euler's method, Multiple choice does not match my answer.

This is the original question. Use Euler's method with h=0.2 to estimate y when x =1 if $y' = (y^2-1) /2$ and y(0) = 0 A. 7.690 B. 12.730 C. 13.504 D. 90.676 My answer follows. n= 5, h= 0.2 a= x_0= ...
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### Numerical integration of differential equation in state-space form

I'm using numerical integration methods like Explicit/Implicit Euler, Runge-Kutta to solve a system of linear ordinary differential equations in state-space representation $\dot{x}=A\,x + B\,u$. I ...
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### Calculating brownian motion in Eulers method

Say for example we have brownian motion term added to an expression $W(t)$ and our $t=2$, what would $W(2)$ be? I' ve tried searching the internet but I can't seem to find a way that gives a formula ...