Method of fundamental solution

Imagine you have a big problem to solve, like trying to figure out how to make a toy robot move. You can try to solve this problem by using a very special method called the method of fundamental solution.

First, you need to know what a fundamental solution is. A fundamental solution is like a magic trick that can help you solve a problem easily. In our example, the fundamental solution would be a special trick to make the toy robot move.

Now, when you use the method of fundamental solution, you think of the big problem you want to solve as being made up of many smaller problems, kind of like how a big puzzle is made up of many little pieces. Each of these smaller problems is called a "source" and they all have different strengths.

So, to solve the big problem, you imagine that all the sources are spread out in a special way around the problem. It's like you have a bunch of little toys robots and you put them all around the big robot to help it move. Each of these little robots is a source.

Then comes the really cool part. Each source sends a special signal to the big robot. This signal tells the robot how to move. But here's the trick. The signals are not the same everywhere, they change depending on how close or far away the sources are from the big robot.

Now, you add up all these signals from all the sources. Remember, each signal is different depending on how close or far away the source is. This means that when you add them up, some of them will cancel each other out and some of them will add together to make the big robot move in the right way!

So, by using this method of fundamental solution, you can solve big problems like making a toy robot move by breaking them down into smaller problems called sources and using their special signals to make the big problem easier to solve. It's like having a bunch of little tricks that you put together to do something really cool!