The given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes.is false.
What is a stiff equation
While integrating a differential equation numerically, one would expect the requisite step size to be relatively small in a region where the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with slope approaching to be zero. This is not always true in all the cases. In some cases 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 very small level in a region where the solution curve is too smooth. The phenomenon is known as stiffness.
So, 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.
Therefore, the given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. is false.
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