Euler’s Method for Solving Differential Equations
Euler’s Method is a simple and straightforward numerical technique used to solve first-order ordinary differential equations (ODEs). This method is particularly useful for obtaining an approximate solution when an exact analytical solution is difficult or impossible to find.
Overview of Euler’s Method
Euler’s Method is based on the idea of using the tangent line at a known point to estimate the value of the function at the next point. It uses the following iterative formula:
[ y_{n+1} = y_n + h \cdot f(x_n, y_n) ]
where:
- ( y_{n+1} ) is the estimated value of the function at ( x_{n+1} ).
- ( y_n ) is the known value of the function at ( x_n ).
- ( h ) is the step size.
- ( f(x_n, y_n) ) is the value of the derivative at ( (x_n, y_n) ).
Watch the full tutorial video:
Link of the downloaded script file: Examples Directory