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What is stiffness in ODEs?
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. Stiff ode solvers do more work per step, but take bigger steps. …
What is a stiff PDE?
In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
What is unit of stiffness?
Explanation: Stiffness is the resistance to deflection. It is the ratio of force (unit N) to the extension (m). Hence its unit is N/m.
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.
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.
Can a stiff equation be a property of the exact solution?
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.
Which is the stiffest differential equation in MATLAB?
We will start with ode45, the workhorse of the MATLAB ODE suite. If δ is not very small, the problem is not very stiff. Try δ = 0.01 and request a relative error of 10 − 4. With no output arguments, ode45 automatically plots the solution as it is computed.