Euler's method is a numerical method for solving ordinary differential equations (ODEs). It approximates the solution by breaking down the interval into smaller segments and using the first-order Taylor series to estimate the next point on the curve.
Euler's method works by using the derivative of the function at a certain point to estimate the value of the function at the next point. This process is repeated until the desired interval is reached, resulting in an approximation of the solution to the differential equation.
Euler's method is relatively simple to understand and implement, making it a popular choice for solving simple differential equations. It also allows for quick and easy calculation of the solution at a specific point without the need for advanced mathematical techniques.
One of the main limitations of Euler's method is that it is only accurate for small intervals. As the interval size increases, the error in the approximation also increases. It also cannot handle systems of differential equations or equations with complex solutions.
To use Euler's method, you will need to know the initial value of the function and its derivative at a specific point. Then, you can use a formula to calculate the next point on the curve and continue this process until the desired interval is reached. The more intervals you use, the closer your approximation will be to the actual solution.