# 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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### An error bound for the Euler method

The question is from the chapter about numerical integration in Stoll. enter image description here The problem says that we can find a bound when we use the areas of rectangles to approximate an ...
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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 ...
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### Euler's method to approximate a differential equation $\frac{dy}{dx} = x - y$

Question: Use Euler's method to find approximate values for the solution of the initial value $-$ problem $$\frac{dy}{dx} = x-y$$ $$y(0)=1$$ on the interval $[0,1]$ using five steps of size $h = 0.2$. ...
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### Higher-order corrections for Euler's method

I would like to preface my question by confessing that I come from a Physics background, so I apologize for any abuse of notation. Given a 1st order ODE $$y' = f(x, y)$$ we can use Euler's Method to ...
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Consider the IVP $$\frac{dy}{dt}(t)=f(t,y(t)), \quad t\in [a,b], \quad y(a)=\alpha \in \mathbb{R}.$$ One can show that Euler's method, i.e., the scheme y_{i+1}=y_i+hf(t_i.y_i), \quad y_0=\alpha, \... 1answer 150 views ### How can I use Euler's Method in order to find the value of a constant k given the differential equation? So, I am trying to attempt part b of this problem using my answer from part a. I just want to confirm if I did part a correctly and how I can do part b? 2answers 56 views ### is Euler's method stable for this problem? Consider the IVP \begin{align*} y''=-y \end{align*} for t \geq 0, and y(0)=1, y'(0)=2. I have rewritten this differential equation as a system of first-order ODE's such that \begin{align*} u'=... 1answer 113 views ### Determining step size for Euler's method. I have completed part(a) to find the y-Lipschitz constant L=3, I'm just not sure how to start part (b), determining a step size to guarantee a global error less than 10^{-3}. Any help would be ... 2answers 139 views ### Exact solution and Euler method approximation for a first order differential equation Having trouble wrapping my brain around this question.. don't know where to start. A. Consider the differential equation f'(x) = (x + 1)f(x) with f(0) =1. What is the exact formula for f(x)? ... 1answer 86 views ### Writing a second order ODE as a system of first order ODEs and applying one step of Euler's method I have been struggling with this problem for awhile now and I just can't seem to get the hang of it. The problem: Write the problem as a system of the first order and perform a step with Euler's ... 0answers 35 views ### Solving kinematic ODEs I am making a particle filter implementation using the kinematic equations as my state transition function, that is to say: \dot{p} = v\\ \dot{v} = a $$where a is assumed to be given. My first ... 1answer 74 views ### Euler's method for concave and monotonic increasing functions? Will Euler's method (implicit or explicit) always approximate a function on or above the real solution, if the function is concave and monotonous increasing? It looks like that in my examples (all ... 1answer 62 views ### Determining graphed solution to Euler's method is incorrect? A sample differential equations exam shows a y-t graph for dy/dt = f(y) with the initial condition y(0) = 2, wherein the plot was was determined using Euler's method. The sample answer states where ... 1answer 88 views ### Compute approximation of ODE using one step of explicit/implicit Euler method I'm given the IVP:$$u^{(3)}(t) + u'(t) = tu(t)u''(2) = 2u(2) = 0u'(2) = 1$$and am asked to approximate the solution for t=2.5 using one step of the explicit Euler-method and one ... 1answer 181 views ### Understanding proof of Euler method having consistency of order 1 In my current lecture we derived that the Euler method has consistency of order 1. At one point in the proof it reads: If f \in C^1(D) on a compact set D around the graph of u, we can bound ... 1answer 148 views ### Numerical integration of differential equation on the surface of a sphere I'm trying to simulate the motion of a particle (a position vector) that is constrained to living on the surface of a unit sphere. Each time-step, \Delta t, the particle moves in some direction on ... 1answer 51 views ### Solve initial value problem I have an exercise that I do not understand. We have to solve an initial value problem:$$ \begin{array}{ccl} y'(t) &=& f(t,y(t)) \\ y(a) &=& y_0 \end{array}  We have to derive ...
Apply Euler's method on the initial value problem $y'(t)=y(t)$ with $y(0)=1$ (in the interval $[0,1]$) and equidistant grid $I_h$, $h=\frac1n$. Give the approximation $y_h$ explicitly. This question ...