Contents
What is a stiff model?
Generally stiffness can be discribed as having time constants in a model that vary by several orders of magnitude. Different algorithms are used for stiff and non-stiff solvers and they each have their own unique stability regions. Stiff differential equations are best solved by a stiff solver, and vice-versa.
What does Stiff problem mean?
An ordinary differential equation problem is stiff if the solution being sought is varying slowly, but there are nearby solutions that vary rapidly, so the numerical method must take small steps to obtain satisfactory results. Stiffness is an efficiency issue.
Is stiffness and modulus the same?
The elastic modulus measures the stiffness in a material, but strength is a function of the modulus. Remember, strength measures how much stress the material can handle before permanent deformation or fracture occurs, whereas the stiffness measures the resistance to elastic deformation.
Which is the best method for stiff equations?
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 are stiff methods used in MATLAB equations?
Stiff methods are implicit. At each step they use MATLAB matrix operations to solve a system of simultaneous linear equations that helps predict the evolution of the solution. For our flame example, the matrix is only 1 by 1, but even here, stiff methods do more work per step than nonstiff methods. Figure 2. A stiff solver requires only 99 steps.
Is the step size needed for a stiff equation?
For some problems this is not the case. In order for a numerical method to give a reliable solution to the differential system sometimes the step size is required to be at an unacceptably small level in a region where the solution curve is very smooth. The phenomenon is known as stiffness.
When is a differential equation a stiff problem?
An ordinary differential equation problem is stiff if the solution being sought is varying slowly, but there are nearby solutions that vary rapidly, so the numerical method must take small steps to obtain satisfactory results. Stiffness is an efficiency issue.