What is meant by stiff Ode?

Stiff ODE. A stiff ODE is defined as one for which the magnitude of the maximum eigenvalue of its Jacobian is much greater than that of the mininmum.

What is stiff?

An induvidual who is often circulates in right wing circles and is characterised by his or her bald head, avoidance of amusement and is generally regarded as an absolute twat Al Gore is a real stiff. He sickens me

What is a stiff equation?

Stiff equations are equations where certain implicit methods, in particular BDF, perform better, usually tremendously better, than explicit ones. (C. F. Curtiss & J. O. Hirschfelder (1952): Integration of stiff equations. PNAS, vol. 38, p. 235-243) The Wikipedia article on stiff equations goes on to attribute the following statements to Lambert:

How do you use stiffly in a sentence?

Beat the egg whites until they are stiff. Our host seemed somewhat stiff. The troops encountered stiff resistance. She managed to keep a stiff upper lip even as everything fell apart. “Excuse me,” he said stiffly. She was scared/bored stiff. The shirt was frozen stiff. We were frozen stiff by the time we got indoors.

How to determine if an ode is stiff or not?

In applications you usually find out if your ODE is stiff by numerically integrating it and watching Runge Kutta fall apart. Then you find the eigenvalues of the linearized DE and realize after the fact you have a stiff system. Then you grumble as you program in your stiff numerical solvers.

How stiff are 2D linear ODE systems?

Both 2d linear ODE systems from above are stiff (i. e. hard to solve with explicit methods) on relative big time intervals (e. g. [0,1]). The linear systems with large stiffness ratio can be considered more stiff because most likely one needs to integrate them on large time interval.

What is the meaning of stiffness?

Stiffness is a subtle, difficult, and important - concept in the numerical solution of ordinary differential equations. It depends on the differential equation, the initial conditions, and the numerical method. Dictionary definitions of the word stiff involve terms like not easily bent, rigid, and stubborn.

Why is ode45 a nonstiff solver?

This is why ode45 is classified as a nonstiff solver along with ode23 and ode113. Solvers that are designed for stiff ODEs, known as stiff solvers, typically do more work per step. The pay-off is that they are able to take much larger steps, and have improved numerical stability compared to the nonstiff solvers.

What is a stiff system of equations?

Popular Answers (1) For linear systems, a system of differential equations is termed stiff if the ratio between the largest and the smallest eigenvalue is large. A stiff system has to treated numerically in a different way than a normal system.

What is an example of stiff differential equation?

One of the most prominent examples of the stiff Ordinary differential equations (ODEs) is a system that describes the chemical reaction of Robertson: there is no problem in numerical integration. However, if the interval is very large (10 11 say), then many standard codes fail to integrate it correctly.

What is the definition of stiffness?

It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution. For linear systems, a system of differential equations is termed stiff if the ratio between the largest and the smallest eigenvalue is large.

Is stiffness a property of the exact solution?

The phenomenon is known as stiffness. In some cases there may be two different problems with the same solution, yet one is not stiff and the other is. The phenomenon cannot therefore be a property of the exact solution, since this is the same for both problems, and must be a property of the differential system itself.

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