Numerical continuation
Hey kiddo, are you ready to learn about numerical continuation? It's a big word, but don't worry, I'll explain it to you like you're five years old!
Numerical continuation is like drawing a picture. Imagine you have a blank piece of paper and you want to draw a picture of a cat. You start by drawing the head, then the body, legs, and tail. This is called "continuation" because you're continuing to draw the cat until it's complete.
Now imagine you want to draw a picture of a cat that's standing on its hind legs. You might not know how to draw this, but you can use numerical continuation to help you. You start by drawing the cat standing normally, then change the position of the legs a little bit, and draw another cat. You keep doing this, making small changes each time until you've drawn the cat standing on its hind legs.
Numerical continuation is like that. It helps us find solutions to problems by making small changes to the input and seeing how the output changes. We start with a known solution, and then make small adjustments to the problem until we find a new solution. We keep doing this until we've found all the solutions to the problem.
For example, let's say we have an equation that we want to solve. We know one solution to the equation, but we want to find more. We make a small adjustment to the equation and see what the new solution is. Then we make another small adjustment and find another solution. We keep doing this until we've found all the solutions.
That's numerical continuation in a nutshell. It's a tool that helps us find solutions to problems by making small adjustments and seeing how the output changes. Pretty cool, huh?
Numerical continuation is like drawing a picture. Imagine you have a blank piece of paper and you want to draw a picture of a cat. You start by drawing the head, then the body, legs, and tail. This is called "continuation" because you're continuing to draw the cat until it's complete.
Now imagine you want to draw a picture of a cat that's standing on its hind legs. You might not know how to draw this, but you can use numerical continuation to help you. You start by drawing the cat standing normally, then change the position of the legs a little bit, and draw another cat. You keep doing this, making small changes each time until you've drawn the cat standing on its hind legs.
Numerical continuation is like that. It helps us find solutions to problems by making small changes to the input and seeing how the output changes. We start with a known solution, and then make small adjustments to the problem until we find a new solution. We keep doing this until we've found all the solutions to the problem.
For example, let's say we have an equation that we want to solve. We know one solution to the equation, but we want to find more. We make a small adjustment to the equation and see what the new solution is. Then we make another small adjustment and find another solution. We keep doing this until we've found all the solutions.
That's numerical continuation in a nutshell. It's a tool that helps us find solutions to problems by making small adjustments and seeing how the output changes. Pretty cool, huh?