• Wrong document? Swap it for free
  • Written by students who passed
  • Immediately available after payment
  • Read online or as PDF
  • 4.6 TrustPilot
0
Sell
Where do you study
Your language
Start selling Create your account
  • The University Of Edinburgh (ED)
  • Numerical Partial Differential Equations
To add items to your wishlist, you must be logged in
Document preview thumbnail
Preview 2 out of 15 pages
Summary

Summary Numerical Partial Differential Equations — Complete Module Revision Guide

0.0
(0 reviews)
- sold
15 pages
2025/2026 Written for academic year
Institution
The University Of Edinburgh (ED)
Module
Numerical Partial Differential Equations
Document preview thumbnail
Preview 2 out of 15 pages

Numerical Partial Differential Equations — a rigorous applied mathematics/numerical analysis module covering the full theory and derivation of finite difference methods for PDEs. Written as a complete, restructured revision guide (not raw lecture notes) — organised by topic for efficient exam preparation, covering the full syllabus in 15 pages with full derivations and worked examples throughout. Index of topics covered: 1. Classification of PDEs (hyperbolic, elliptic, parabolic) 2. Finite differences for ODEs: consistency, stability & convergence 3. The method of lines and the heat equation (forward Euler, backward Euler, Crank-Nicolson) 4. Boundary conditions (Dirichlet, Neumann, mixed) 5. Finite differences for elliptic PDEs (Poisson equation, five-point Laplacian) 6. Spectral methods (non-examinable overview — Fourier & Chebyshev methods) 7. Iterative methods for linear systems (Jacobi, Gauss-Seidel, steepest descent, conjugate gradients) 8. Hyperbolic PDEs and the advection equation (characteristics, upwind schemes, Courant number) This guide includes full mathematical derivations (not just definitions) for the key theorems of the course — including the fundamental "consistency + stability = convergence" theorem, the stability condition for forward Euler applied to the heat equation, and the convergence rate of the conjugate gradient method. Suitable for students studying numerical analysis, numerical methods for PDEs, or applied/computational mathematics modules with similar content.

Content preview

Numerical Partial Differential
Equations
Complete Revision & Study Guide

A topic-by-topic guide covering PDE classification, finite difference methods, stability theory,
elliptic and parabolic problems, iterative linear solvers, and hyperbolic PDEs — with full
derivations and worked examples throughout.



Original study notes — independently written summary and explanation

, Contents

• 1. Classification of PDEs
• 2. Finite Differences for ODEs: Consistency, Stability & Convergence
• 3. The Method of Lines and the Heat Equation
• 4. Boundary Conditions
• 5. Finite Differences for Elliptic PDEs
• 6. Spectral Methods (non-examinable overview)
• 7. Iterative Methods for Linear Systems
• 8. Hyperbolic PDEs and the Advection Equation

Document information

Study
Unknown
Uploaded on
September 21, 2026
Number of pages
15
Written in
2025/2026
Type
Summary
Report Copyright Violation
$14.54
Wrong document? Swap it for free Within 14 days of purchase and before downloading, you can choose a different document. You can simply spend the amount again.
Written by students who passed
Immediately available after payment
Read online or as PDF
Seller avatar
thegradientdescentnotes
Sold
0
Followers
0
Items
8
Last sold
-

Browse related subjects

Subjects

  • numerical pdes
  • pde classification
  • finite difference methods
  • finite differences
  • consistency stability
  • convergence
  • lax richtmyer stability
  • von neumann analysis
  • numerical partial differential equations
  • m

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their exams and reviewed by others who've used these revision notes.

Didn't get what you expected? Choose another document

No problem! You can straightaway pick a different document that better suits what you're after.

Pay as you like, start learning straight away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

Student with book image

“Bought, downloaded, and smashed it. It really can be that simple.”

Alisha Student

Working on your references?

Create accurate citations in APA, MLA and Harvard with our free citation generator.

Learn more Create citation
Working on your references?

Frequently asked questions