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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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 ...
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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 $\...
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805 views

Finding correct step-size for the Euler method

I don't understand how to find the correct step-size $h$ for the Euler method. My script says the following: One method consists in computing the numerical solution for an arbitrary $h$ and then $...
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285 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 ...
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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 ...
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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 ...
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177 views

Stability analysis for eulers method for second order differential equation

I need an example for stability analysis of Euler's method for second order ODE.. thanks alot
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49 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 ...
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Using Eulers method to solve equation of motion of aircraft

I am told I can solve the following differential equation by utilising Euler's method. I can solve simple differential equations with the method, I am however, having some trouble wrapping my head ...
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Problem - how to find λ?

Guys I need some help with this problem, I tried a thousand times but I couldn't find a realistic answer. Solve numerically: x'=-λ.x.y Where: n=x+y=500; x0= 499 (initial condition); with x=people ...
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132 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 ...
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152 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 ...
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28 views

How do I calculate an approximation of the solution of the begining values at the point t = 1 with Euler method?

I have already posted question where I was asking about sketching Euler method. The explicit Euler method for numerically solving the begining values of differential equation $x′=f(t,x),x(t_0)=x_0$ ...
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873 views

Error Bound for Euler's Method

I'm studying the Euler Method trough the book "Numerical Analysis", but I didn't understand an example where we have to calculate the error of this method... First of all we have a Corollary which ...
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130 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 ...
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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 $x(1)$ ...
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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)...
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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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84 views

Understanding definition of explicit Euler method

I'm quite new to ODE and the IVP (initial value problem), so I've some doubts related to these topics. I'm reading a draft provided by my professor which talks about the "polygon" or explicit Euler ...
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46 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 $1\le x\le 2$?
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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 ...
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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 ...