# Questions tagged [stiffness]

Referring to ordinary differential equations that require an extremely small timestep to guarantee numerical stability.

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### Pretension a truss mechanism (using the direct stiffness method)

Currently, I'm working on a mechanical mechanism where nodes are connected via beams. This is very comparable to planar truss mechanism analysis, but in my case, the deformations are large (relative ...
586 views

### Why do I get an oscillatory solution when applying the implicit trapezoidal method to the linear diffusion equation?

I wish to solve the following equation, $$\frac{\partial f}{\partial t}=\frac{\partial}{\partial x}\left(D(x)\frac{\partial f}{\partial x}\right)$$ using an exponential integrator. I discretize this ...
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1 vote
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### Exponential Integrator to solve PDE with Stiff term

I wish to solve an equation like the following, $$\frac{\partial f}{\partial t}+\frac{\partial}{\partial x}\left(A(x)f\right)=S(x,t)f$$ where $A(x,f)f$ and $S(x,t)f$ are the advection and the source ...
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### Using backward and forward Euler method to solve a certain stiff ODE

When using the backward and forward Euler methods to solve a certain stiff differential equation, what criteria does one look at before drawing the conclusion that one is more stable than the other?
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### Are stiffness and instability equivalent?

To the best of my knowledge, stiffness of ordinary differential equations is difficult to capture but can be roughly described as problems where explicit methods don't work while implicit ones do. ...
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### Solving detailed combustion kinetics in CFD, where to start?

I have some experience solving single- and multicomponent Euler equations for modeling of gas flows, including combustible ones. The code (variations of finite-difference WENO methods) is written with ...
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### In FEM, why is the stiffness matrix positive definite?

In FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation? For instance, we can consider the ...
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### Spectral Collocation (or Weighted Residual) Methods to solve Stiff ODEs?

I have a system of ODEs which is (at least moderately) stiff. Consider the class of spectral collocation methods https://en.wikipedia.org/wiki/Spectral_method or the related class of weighted ...
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### Does the global stiffness matrix size depend on the number of joints or the number of elements?

When assembling all the stiffness matrices for each element together, is the final matrix size equal to the number of joints or elements?
769 views

### What is the case of trade-off in different Runge-Kutta methods

There are so many Runge-Kutta methods, including Dormand-Prince 45, Cash-Karp 54, Fehlberge 78. Is there any comparison between them? E.g. What is each approach sacrificing? What is the general ...
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### RK4 for stiff IVP

I need a solver of stiff Inital-Value Problems (IVP) in python exploiting RK4 preferably explicit. I have been searching for past few days but could not find it. Following are my queries: Does the ...
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1 vote
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### Resources for viscous behavior in simple FEM

I am working on a simple explicit-integration lumped-mass elastic FEM code which implements CST+DKT triangles (plate+shell) and constant-strain tetrahedra (http://woodem.eu/doc/theory/membrane-element....
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