Mathematics - iii (Differential Calculus) - Vol 4 | 11. Heun’s Method by Abraham | Learn Smarter
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11. Heun’s Method

11. Heun’s Method

Numerical methods play a crucial role in solving ordinary differential equations (ODEs) that cannot be solved analytically. Heun's Method, also known as the improved Euler's method, offers a second-order technique that enhances accuracy by averaging slopes at the beginning and end of intervals. This method is essential in engineering applications where precision is vital.

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  1. 11
    Numerical Solutions Of Odes

    Heun's Method is a second-order numerical method for solving ordinary...

  2. 11.1
    Heun’s Method

    Heun's Method is a second-order numerical technique for solving ordinary...

  3. 11.1.1
    Introduction

    Heun's Method is a second-order numerical approach used for solving ordinary...

  4. 11.1.2
    Mathematical Background

    Heun’s Method is a second-order numerical technique utilized for solving...

  5. 11.1.3
    Heun's Method Formula

    Heun's method is a second-order numerical technique for solving ordinary...

  6. 11.1.4
    Algorithm: Step-By-Step Implementation

    This section outlines the step-by-step implementation of Heun’s Method, a...

  7. 11.1.5
    Example Problem

    This section presents an example of using Heun's Method to solve an ordinary...

  8. 11.1.6
    Geometric Interpretation

    Heun's Method provides a geometric interpretation by averaging slopes to...

  9. 11.1.7
    Comparison With Euler’s Method

    Heun’s method improves the accuracy of Euler’s method for solving ODEs by...

  10. 11.1.8
    Advantages Of Heun’s Method

    Heun’s Method is a second-order numerical technique for solving ordinary...

  11. 11.1.9

    Heun’s method offers improved accuracy over Euler’s method, yet it has its...

  12. 11.1.10
    Applications

    Heun's Method is a versatile numerical technique for solving ordinary...

  13. 11.1.11

    Heun’s Method is a second-order numerical technique for solving ordinary...

What we have learnt

  • Heun’s Method is a second-order improvement over Euler’s method for numerically solving ODEs.
  • It utilizes a predictor-corrector approach to refine estimates by averaging slopes.
  • Heun's Method balances efficiency and accuracy, making it suitable for a variety of engineering applications.

Key Concepts

-- Ordinary Differential Equations (ODEs)
Equations involving functions and their derivatives which describe how a quantity changes over time.
-- Heun's Method
A numerical technique that improves upon Euler's method by using an average of slopes to enhance accuracy.
-- PredictorCorrector
A two-step process in numerical analysis where an initial estimate is refined to improve accuracy.
-- Stability
A measure of how errors in numerical solutions behave as they propagate through calculations.

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