Lecture notes on Finite Difference Methods

In summary, the conversation discusses the use of Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque in Numerical Analysis. A physicist recommended the book, but the chapters can be challenging to understand. The person is looking for supplement materials such as slides or lecture notes, and it is suggested to try Wikipedia or writing code to solve equations for better understanding.
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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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  • #2
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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1. What are Finite Difference Methods?

Finite Difference Methods are numerical techniques used to approximate solutions to differential equations. They involve dividing a continuous domain into a finite number of discrete points and approximating the derivatives at those points using algebraic equations.

2. What types of problems can be solved using Finite Difference Methods?

Finite Difference Methods are commonly used to solve problems in physics, engineering, and other fields that involve differential equations. They can be applied to a wide range of problems, including heat transfer, fluid flow, and structural analysis.

3. How do Finite Difference Methods work?

Finite Difference Methods work by approximating the derivatives in a differential equation using a finite difference formula. This involves calculating the values of the function at a set of discrete points and using these values to approximate the derivatives at those points. The accuracy of the solution depends on the number of points used and the choice of finite difference formula.

4. What are the advantages of using Finite Difference Methods?

Finite Difference Methods are relatively easy to implement and can provide quick and accurate approximations to solutions of differential equations. They also allow for the use of computers to solve complex problems that would be difficult or impossible to solve analytically.

5. Are there any limitations to using Finite Difference Methods?

Finite Difference Methods may not always provide accurate solutions, especially for problems with complex geometries or boundary conditions. They also require a significant amount of computational resources, which can be a limitation for large-scale problems. Additionally, they may not be suitable for problems with discontinuities or singularities.

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