Improved Euler's Method to Solve First Order Ordinary Differential Equation in Numerical Analysis

Improved Euler's Method for Solution of First Order Ordinary Differential Equation ODE in Numberical Analysis 2 ‪@mutualacademy313‬ In this lecture, we explain the Improved Euler’s Method (also called the Heun’s Method) for solving first-order ordinary differential equations (ODEs). This method gives more accurate results than the basic Euler’s Method by taking the average of slopes at the beginning and end of each interval. We walk through the complete formula, explain its derivation and logic, and solve step-by-step examples to show how the method works in practice. This topic is vital for students of BS Mathematics (8th Semester – GCUF) and MSc Mathematics (4th Semester) in Numerical Analysis 2. At Mutual Academy, we break down advanced math into simple concepts using a Urdu-English mix to help students deeply understand and apply each topic. Don’t forget to subscribe and follow the full series on Numerical Methods! Related Searches: Improved Euler’s method step by step Heun’s method for ODE Solve ODE using improved Euler Average slope method in differential equations Numerical solution of dy/dx = f(x, y) BS Math 8th semester GCUF Numerical Analysis MSc Math 4th semester Numerical methods Improved Euler vs Euler method Mutual Academy ODE lectures Numerical Analysis 2 techniques