Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [eulers-method]

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

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

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How does Euler's method work when step size and wanted values are different?

I have a question that goes as such: Use Euler’s method with $dt= 0.1$, to estimate $p$ for these values of $t$, using initial condition $(0,5)$. $t= 2,4,6,8,10,12,14,16$ $\frac{Dp}{dt}= 0.05(p-4)(12-p)$ I am unsure how to solve because $dt=0.01$…
user1117467
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Forward Euler Method Given Two Step Sizes

I am attempting to compute an approximation of the solution with the forward Euler method in $[0,1]$ with step lengths $h_{1}= 0.2$, $h_{2}= 0.1$ given the initial value problem below $$\frac{dy}{dz}=\frac{1}{1+z}-y(z)\quad y(0)=1$$ I am not sure…
dsapprentice
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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 values $y_s$ if I try to integrate this problem with a…
Patrick
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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 an attempt, however, what I am most confused on is…
Liam Carrington
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Forward Euler and 1st-order linear ODE with exponential solution

Let us consider the simple ODE $y'=y$ with $y(0)=1$ on the interval $[0,1]$. The solution is obviously $y(t)=\mathrm{e}^t$. Now, consider a Forward Euler approximation of the solution to the ODE. The sequence $y_k=(1+h)^k$ with $h=1/n$, $n$ being…
pluton
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