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

  • 11

    Numerical Solutions Of Odes

    Heun's Method is a second-order numerical method for solving ordinary differential equations that improves upon Euler's Method by utilizing an average slope for better accuracy.

    Learning Practice

  • 11.1

    Heun’s Method

    Heun's Method is a second-order numerical technique for solving ordinary differential equations (ODEs) with improved accuracy compared to Euler's method.

    Learning Practice

  • 11.1.1

    Introduction

    Heun's Method is a second-order numerical approach used for solving ordinary differential equations (ODEs) with better accuracy than Euler's method.

    Learning Practice

  • 11.1.2

    Mathematical Background

    Heun’s Method is a second-order numerical technique utilized for solving ordinary differential equations (ODEs) more accurately than Euler’s method.

    Learning Practice

  • 11.1.3

    Heun's Method Formula

    Heun's method is a second-order numerical technique for solving ordinary differential equations (ODEs) that improves accuracy over Euler's method.

    Learning Practice

  • 11.1.4

    Algorithm: Step-By-Step Implementation

    This section outlines the step-by-step implementation of Heun’s Method, a second-order numerical technique for solving ordinary differential equations (ODEs).

    Learning Practice

  • 11.1.5

    Example Problem

    This section presents an example of using Heun's Method to solve an ordinary differential equation, showing its application and effectiveness.

    Learning Practice

  • 11.1.6

    Geometric Interpretation

    Heun's Method provides a geometric interpretation by averaging slopes to improve accuracy over Euler's Method.

    Learning Practice

  • 11.1.7

    Comparison With Euler’s Method

    Heun’s method improves the accuracy of Euler’s method for solving ODEs by employing a two-step predictor-corrector approach.

    Learning Practice

  • 11.1.8

    Advantages Of Heun’s Method

    Heun’s Method is a second-order numerical technique for solving ordinary differential equations (ODEs) that offers better accuracy and stability compared to Euler's method.

    Learning Practice

  • 11.1.9

    Limitations

    Heun’s method offers improved accuracy over Euler’s method, yet it has its limitations in terms of function evaluations and applicability to stiff equations.

    Learning Practice

  • 11.1.10

    Applications

    Heun's Method is a versatile numerical technique for solving ordinary differential equations (ODEs), particularly suitable for engineering applications.

    Learning Practice

  • 11.1.11

    Summary

    Heun’s Method is a second-order numerical technique for solving ordinary differential equations (ODEs), improving accuracy over Euler's method.

    Learning Practice

References

unit 5 ch4.pdf

Class Notes

Memorization

What we have learnt

  • Heun’s Method is a second-o...
  • It utilizes a predictor-cor...
  • Heun's Method balances effi...

Final Test

Revision Tests