From the course: Complete Guide to Differential Equations Foundations for Data Science

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Stability and convergence

Stability and convergence

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Stability and convergence

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- [Instructor] Now that you've learned about three common numerical methods, let's take a moment to review a few key aspects about them. More specifically, let's take a look at their stability and convergence. Let's start off by looking at a definition of stability. You've heard me mention stability with these different numerical methods, but what does this mean exactly? Stability measures if a numerical method remains well-behaved over time or easily diverges uncontrollably. If a numerical method is stable, then small changes in initial conditions or round-off errors will not cause it to have errors grow exponentially as more iterations are made. So what can affect the stability of a numerical method? The step size can affect the stability. The numerical method used can affect the stability. And finally, the nature of the differential equation being solved. For example, the stiff equation. Let's look at the stability for each of the three numerical methods you explored. For Euler's…

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