# 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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### Stability: Backwards vs (normal) Euler method

Why is backwards Euler method more stable than the (normal) Euler method? The only thing that changes in the creation of each method is that the approximation of the derivative is taken "from behind" (...
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### Euler method to geometric brownian motion stochastic diferential equation

I am doing Mark Joshi's Concepts and Practice of Mathematical Finance, project $1$ Vanilla options in a Black-Scholes world. At the final part of the project, we have the following: One further ...
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### Determining the maximum stepsize for using the forward euler method

I have been given this question: Assume $t \in (3/12,8/12)$ and $W_0 = 1.8$ What is an upper bound for the time step in this scenario? Give an exact value. I haven't been given a differential ...
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### Implicit and explicit Euler Method for expression of stochastic solutions in time T

I have expression for implicit iteration (backward Euler Method): $$X_{n+1} = X_{n}+\delta tX_{n+1}+\sqrt{\delta t}X_{n+1}Z_n,$$ where $n=0,...,N-1; Z_n iid\sim N(0,1)$ and explicit iteration (...
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### implementing Euler method in matlab for second order ODE

I have to use the Euler method for the differential equation : $$\begin{cases} x^{\prime}=y \\ y^{\prime}=-\frac{k}{m}x-\frac{\beta}{m}x^{3} \end{cases}$$ with $k=4, \beta =-0.04 , m=1$ in matlab. We ...
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### 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 ...
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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 ...
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### How to determine the step size using Euler's Method?

Consider the initial value problem $x' = x+e^{-x}$ , $x(0)= 0$. This problem can’t be solved analytically. Using the Euler method, compute $x$ at $t = 1$, correct to three decimal places. How ...
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### 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 ...
Fixed point iteration is sometimes used for solving the implicit Euler method $$y_{n+1}^\mathrm{(I)}= y_n + hf(y_{n+1}^\mathrm{(I)})$$ with the iteration procedure starting with explicit Euler $$y_{... 1answer 378 views ### Why does the Euler method go bad when the time step T is decreased? Consider below differential eqn$$\dfrac{dy}{dt} = y$$In discrete form, with a time step T, using forward euler, it becomes$$\dfrac{y[n+1]-y[n]}{T} = y[n]$$Solving the difference eqn we get$$y[...
I'd like to solve the equation $$\phi''(x) = \lambda \sin (\phi(x))$$ where $x \in (0,L)$, $\phi'(0) = 0$, $\phi'(L) = 0$. Let $\psi = \phi'$ and $$\phi'(x) - \psi(x) = 0$$  \psi'(x) - \lambda ...