Mathematics - iii (Differential Calculus) - Vol 4 | 16. Error Analysis in Numerical ODE Solutions by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Academics

Grades

Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Curriculum

CBSE ICSE IB
Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Professional Courses
Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

games
Typing
Memory
Math
English Adventures
Knowledge
16. Error Analysis in Numerical ODE Solutions

Adams-Moulton methods are implicit multistep techniques used for numerically solving ordinary differential equations (ODEs), notable for their enhanced accuracy and stability. These methods work in tandem with Adams-Bashforth methods in predictor-corrector schemes, facilitating improved performance for various types of ODEs. The chapter covers the derivations, common formulas, advantages, disadvantages, and an algorithmic approach, emphasizing the need for an initial predictive step from an explicit method.

Sections

  • 16.1

    What Is The Adams–moulton Method?

    The Adams–Moulton Method is an implicit multistep method used in numerical analysis to solve ordinary differential equations, known for its accuracy and stability.

    Learning Practice

  • 16.2

    Derivation Of The Method

    The derivation of the Adams–Moulton method involves interpolating the function f(x,y) and integrating it to approximate solutions for ordinary differential equations.

    Learning Practice

  • 16.3

    Adams–moulton Formulas

    The Adams–Moulton method is an implicit multistep method used for solving ordinary differential equations (ODEs), known for its accuracy and stability.

    Learning Practice

  • 16.4

    Predictor–corrector Approach

    The Predictor-Corrector Approach utilizes the Adams-Bashforth method for prediction followed by the Adams-Moulton method for correction when solving ODEs.

    Learning Practice

  • 16.5

    Algorithm: Adams–moulton Method (Predictor–corrector)

    The Adams-Moulton method is an implicit multistep approach to numerically solve ordinary differential equations (ODEs), known for its accuracy and stability.

    Learning Practice

  • 16.6

    Worked Example

    This section illustrates the application of the 1-step Adams–Moulton method through a detailed worked example.

    Learning Practice

  • 16.7

    Advantages And Disadvantages

    The Adams–Moulton method offers significant benefits in solving ordinary differential equations, particularly relating to accuracy and stability, but it also comes with drawbacks such as the need for implicit solutions.

    Learning Practice

  • 16.8

    Summary

    The Adams–Moulton methods are implicit multistep techniques widely used for accurately and stably solving ordinary differential equations (ODEs).

    Learning Practice

References

unit 5 ch9.pdf

Class Notes

Memorization

What we have learnt

  • Adams-Moulton methods are u...
  • They provide better accurac...
  • These methods require the i...

Final Test

Revision Tests