Solving Differential Equations Using Euler's Method

MATLAB is a high-level technical computing software platform widely used for solving various mathematical problems, including differential equations. Euler's method serves as a fundamental numerical technique for approximating solutions to differential equations. This approach discretizes differential equations based on their mathematical definition and iteratively computes progressive approximations toward the solution. In MATLAB implementation, Euler's method typically involves defining the differential equation as a function, specifying initial conditions, setting an appropriate step size, and implementing an iterative loop that updates the solution using the formula: y_{n+1} = y_n + h*f(t_n, y_n), where h represents the step size and f(t,y) defines the differential equation. Key functions often utilized include: - Anonymous functions or separate function files to define the differential equation - For loops for iterative calculations - Plotting functions like plot() to visualize the solution progression Through MATLAB's Euler's method implementation, users can efficiently solve various differential equation problems while obtaining accurate numerical solutions with controlled precision through step size adjustments.