Explicit and implicit methods

Think of baking a cake. If you follow a recipe step-by-step and measure out all the ingredients precisely, that's like using an explicit method. You're being very clear and specific about each step you take.

But imagine you want to make a cake without measuring cups or a recipe. You might just have a general idea of what ingredients to use and how long to bake it. That's like using an implicit method - you're relying on your intuition and past experience to guide you.

In math, these two methods are used to solve equations. An explicit method calculates each step very precisely, like following a recipe. An implicit method relies on logical guesses and approximations, like using your intuition to bake a cake.

Both methods have their advantages and disadvantages, depending on the problem you're trying to solve. Explicit methods are usually easier to program and faster to compute, but they can run into errors if the steps aren't calculated precisely enough. Implicit methods may take longer to compute, but they can be more robust and accurate when dealing with more complex equations.