# Questions tagged [stability]

The study of the propagation of errors in a numerical algorithm.

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### Step size and stability of Euler forward method

I'm trying to calculate the maximum step size that provides stability for the following nonlinear IVP using the Euler forward method: $u'(t) = -200tu(t)^2,\qquad u_0 = 1, \qquad t\in [0,3]$, with ...
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### What is the flaw in my stability analysis?

The ODE $${d^2x\over dt^2}=-kx; k>0$$can be converted in the system of linear equations as \begin{align} {dx\over dt} & =v\\ {dv\over dt} &= -kx\\ \end{align} Using Euler’s method, ...
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### Finite Difference Method Limitations/Stability Criteria

Is it possible to solve an equation with only a single derivative such as: $$\frac{\partial U(x,t)}{\partial t} = A - BU(x,t)$$ with finite difference methods? I ask as I am trying to solve the ...
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### How to derive an Implicit Runge-Kutta method from Pade approximation

I was reading some work by Butcher and I came across Pade approximations and the correlation between them and stability functions for some Implicit Runge-Kutta methods. For example, in this Pade table ...
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### Lagrange multipliers space is too rich in a mathematical view

Background: Lagrange multiplier method has been employed in numerous fields, such as contact problems, material interfaces, phase transformation, stiff constraints or sliding along interfaces. It is ...
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### Method to solve linear, first order ODE of generalized matrix matrix form

The equation and its meaning: Consider two sets $(A)_{l=0,...,m_a},$,$(B)_{l=0,...,m_b}$ of hermitian matrices and a set of positive semidefinite matrices $(C)_{l=0,...,m_c}$. Each matrix has the ...
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### Von Neumann analysis for coupled PDE's

I am interested in understanding how to perform stability analysis for coupled (to keep things do-able, lets say linear) PDE's In the case of a single PDE, i understand the logic behind the VN ...