Lecture notes on Finite Difference Methods

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SUMMARY

The discussion focuses on the use of Finite Difference Methods for solving Ordinary and Partial Differential Equations, specifically referencing the book "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J. LeVeque. Participants express the need for supplementary materials, such as slides or lecture notes, particularly for Chapters 2, 3, and 4. A suggestion to utilize Wikipedia as a starting point for additional resources is made, along with the recommendation to practice coding solutions for equations like Laplace's equation in 2D or the wave equation in 1D to enhance understanding.

PREREQUISITES
  • Understanding of Ordinary and Partial Differential Equations
  • Familiarity with Finite Difference Methods
  • Basic programming skills for implementing numerical solutions
  • Access to "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J. LeVeque
NEXT STEPS
  • Research supplementary lecture notes on Finite Difference Methods
  • Explore Wikipedia's resources on Laplace's equation and wave equations
  • Learn coding techniques for implementing Finite Difference Methods in Python or MATLAB
  • Study numerical stability and convergence in Finite Difference Methods
USEFUL FOR

Students and professionals in numerical analysis, mathematicians, physicists, and anyone interested in applying Finite Difference Methods to solve differential equations.

the_dane
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I have lately been working with Numerical Analysis and I am using Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque. It was recommended to me by a friend of mine (physicist)

https://epubs.siam.org/doi/book/10.1137/1.9780898717839?mobileUi=0&
However, Sometimes the chapters can be long and difficult to understand. I was wondering if you guys know any Slides or lecture notes I can use as a supplement for LeVeques book? as of now I am mainly interested in Chapters 2,3,4.
 
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Have you tried Wikipedia? This page is a start. I find the best way to learn is to pick an equation you want to solve (Laplace's equation in 2D or the wave equation in 1d are good places to start), and then write some code to solve it. The act of writing the code is where the learning happens.
 
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