Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [eulers-method]

The tag has no usage guidance.

0
votes
1answer
32 views

Euler's method example: Where this value came from?

So, i've found an example that suits what i want to do, and i understood the majority of it, but i didn't really figured out where the last value, of the last line came from. I wanna know where did ...
0
votes
1answer
53 views

Example of a engineering problem solved using the Euler's method

I'm new to this forum, mechanical engineering and to matlab as well and this will be my first true academic work at university. I'm only at the 1st semester of my course and really need some help. So,...
1
vote
1answer
71 views

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 ...
0
votes
1answer
58 views

Deriving Implicit Euler Method Update Rule to be used in iterations

Starting with the approximation $$y'(t) = \frac{y(t) - y(t - h)}h$$ arriving at an update rule of the form: $$y(t + h) = y(t) + hf(t + h, y(t + h))$$ Derive the implicit Euler update rule for this ...
0
votes
0answers
49 views

How can I prove Euler's formula using mathematical induction

Using Euler's formula in graph theory where $r - e + v = 2$ I can simply do induction on the edges where the base case is a single edge and the result will be 2 vertices. A single edge also has ...
0
votes
1answer
22 views

Trapezoidal iteration method for solving differential equation

I am learning on how to use various numerical methods to approximate solutions to differential equations. We are using R, to actually iterate these functions, but I am having difficulties wrapping my ...
0
votes
1answer
33 views

ODE with Euler Method

I have to solve the following ODE: $y'(t)=y(t)+t$, $y(0)=0$ with Eulers Method in two steps, where $h=0.1$. I tried the following: $y'(0)=y(0)+0=0$ and then I get $y(0.1)=y(0)+h*y'(0)=0$ but then ...
0
votes
0answers
35 views

What's the power of quaternion $[e^{a} * (cos(r) + \frac{sin(r)}{r}(bi+cj+dk)) ]^ 2$?

Euler's identity extended into quaternions is: $q = a + bi + cj + dk$ with a,b,c,d real numbers for the below: $\sqrt{b^2+ c^2 + d^2} = r > 0$, and $\frac{bi+cj+dk}{r}$ = $\sqrt{-1}$, ...
1
vote
0answers
114 views

Using Quaternion Extension of Eulers Formula what is $e^{qw} * e^{qw} = e^{qw2}$?

Knowing that for quaternions Euler's identity is: $q = a + bi + cj + dk$ with a,b,c,d real numbers $\sqrt{b^2+ c^2 + d^2} = r > 0$ $e^q = e^{a + r\sqrt{-1}} = e^ae^{r\sqrt{-1}} = e^a(...
-1
votes
1answer
31 views

Homework Problem Help with Euler's Formula

I have a question with my homework. I'm pretty sure I have to use Euler's formula to solve it, but I'm kind of stuck on how to use the formula to solve this problem. I started to draw the problem on ...
2
votes
1answer
86 views

Euler's method for different differential equations

I have equation: \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}t} = -0.04\sqrt{y} \end{align*} How would I find the expression for Euler's method? I know the general expression is: $$y_n=y_{n-1}+h\...
1
vote
0answers
18 views

Local stability analysis for a differential equation

I am trying to perform a local stability analysis for the differential equation $$dy/dt = tcos(y)+e^{-t}$$ I want to determine the step size I will need at a particular time t and corresponding ...
2
votes
1answer
271 views

Is Backward-Euler method considered the same as Runge Kutta $2^{\text{nd}}$ order method?

I have a book that quotes: Euler's method, Modified Euler's method and Runge's method are Runge-Kutta methods of first, second and third order respectively. The fourth-order Runge-Kutta method ...
1
vote
0answers
36 views

Using Euler's method to estimate a value of y(1.1) if y(1,0) = 0.

I am currently attempting some past paper exam questions and have come across a question on Euler's method that I am unsure on how to solve. This is the question; MCQ on Euler's Method: I have had ...
0
votes
0answers
20 views

Finding a Function Given a Piece

Suppose you're given function on a domain ([1,2] for instance) that exactly resembles $\frac{1}{x}$. Is this enough to know (assuming the function doesn't have a weird behavior, such as piecewise or ...
2
votes
1answer
115 views

Euler's method: plotting total error (round-off included) as a function of stepsize

I'm trying to show that when the stepsize is too small, round-off error accumulates making the total error too big, hence doing the euler method with a smaller stepsize yields better results but only ...
1
vote
1answer
46 views

Max vertices in Odd Degree Graph

If I have a graph whose vertices all have odd degree greater than 1, what is the maximum possible number of vertices if the graph has at most 14 edges? My thought for this is basically that your best ...
0
votes
2answers
41 views

Using Euler derive the relationships between cosine and exponential function [closed]

$$\cos\phi=\frac{1}{2}(e^{j\phi} + e^{-j\phi}).$$ Please i was told to do this assignment but cant prove if anyone can help me out
0
votes
2answers
95 views

Using Complex exponential/Euler's Method to integrate, bizarre case

$ \int e^{-3t} cos(2-\sqrt 3 t) dt $ I have been asked to evaluate that using complex exponential/euler's method. I have done many similar questions but all of them had something like (cos3x), sin(5t)...
1
vote
2answers
584 views

Euler's Method Global Error: How to calculate $C_1$ if $error = C_1 h$

My textbook claims that, for small step size $h$, Euler's method has a global error which is at most proportional to $h$ such that error $= C_1h$. It is then claimed that $C_1$ depends on the initial ...
0
votes
1answer
124 views

Solving coupled system of ODE's

I'm reading a paper on system of ordinary differential equations, and I'm a bit confused with the following definition of a such: $ \dot{\phi} = -A^T\phi-Qx , \quad \dot{x} = \left\{ \begin{array}{ll}...
0
votes
1answer
162 views

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 ...
-3
votes
1answer
63 views

Euler's method to IVP [closed]

The modified Euler's method is $w_{0}=\alpha$, $$w_{n+1}=w_{n}+\frac{h(f(w_{n},t_{n})+f(w_{n}+hf(w_{n},t_{n}),t_{n+1}))}{2}$$. Apply this method to the IVP $$y^\prime=\lambda y,$$ $y(0)=1$, with $\...
1
vote
2answers
200 views

How to rewrite a 2nd order nonlinear ODE into an initial value problem of first order?

I am trying to rewrite the initial value problem $x''(t) = -sin(x(t))$ with initial values $x(0)= \pi/2 $ and $x'(0) = 0 $ into and initial value problem of first order ODE system. Later I will have ...
0
votes
1answer
45 views

Can someone help me derive this equation using Euler's formula?

$e^{a + bi} = e^a(\cos b + i \sin b)$ -- Euler's formula Euler's formula gives rise to $e^{πi} + 1 = 0$ -- Equation Five important numbers of $0, 1,\pi , e$, and $i$ are in this equation. How can ...
0
votes
0answers
24 views

Solution to Recurrence Equation

I have to use $20$ steps of size $h=0.5$ to estimate $y(11)$ for the curve of $y' = x-y$, going through $y(1)=1$. Now, I could just solve the differential equation, but there will be harder ...
1
vote
1answer
45 views

Numerical Solution for ODE with a squared term inhibiting use of Euler's Method

I have this ODE: $$A(x)\ddot{x}+B(x)\dot{x}^2+C(x) = 0$$ $A,B,C$ are functions of $x(t)$. Usually I'd solve this numerically using Euler's method but in this case the $\dot{x}^2$ is giving me ...
1
vote
1answer
129 views

Eulers formula with an infinite series?

Alright so this is a real life problem and not just a homework thing. Ive borrowed money from a family member $16323 \rm dkk$ to be exact. Im borrowing this money for $211$ days and im borrowing it ...
1
vote
2answers
144 views

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 ...
1
vote
1answer
116 views

What is meant by Adams Bashforth being a “boot strap” method?

People seem to say that the Adams-Bashforth method requires some "boot strapping" because it needs two initial conditions: $y_{n+1}=y_n+\frac{\Delta t}{2}[3f(t_n,y_n) - f(t_{n-1}, y_{n-1})]$ I ...
1
vote
1answer
99 views

How to understand where I am going wrong in euler method

I have a question from my book and it says essentially, consider the IVP $x^{\bullet}=-x$ with $x(0)=1$, what is the exact value of x(1), then using Eulers method with step size1 , estimate $x(1)$ ...
-1
votes
2answers
276 views

Eulers method to approximate gravity in one dimension

I am going to program Eulers method in Octave to approximate gravity in 1-dimension. I understand the formula for Eulers method, which is equal to: What I don't understand is what my function $f(t,y)...
0
votes
1answer
44 views

Determing if Euler's Method Overestimates

How do you work out if Euler's method overestimates the actual solution, for the ODE: $\frac{dy}{dx}=24\tan(\pi x)$ With steps of 0.25 from $1\le x\le 2$?
0
votes
1answer
113 views

Why the staggered Euler (Euler-Backward) method is not runge-kutta method?

Why the staggered Euler (Euler-Backward) method is not runge-kutta method? The method is given by $$x_{n+1}=x_n+hg(p_{n+1})$$ $$p_{n+1}=p_n+hg(x_n)$$ I am not very familiar with the conditions of ...
4
votes
1answer
2k views

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 ...