Lecture Notes · Lecture Notes
MIT OpenCourseWare
Numerical Methods for Partial Differential Equations
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Dr. Benjamin Seibold
- Term
- Spring 2009
- Level
- Graduate
- What's inside
- 1 lecture note · 1 reading · 37 other files · 5 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.336 Numerical Methods for Partial Differential Equations, Spring 2009, Dr. Benjamin Seibold — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 26 items is confirmed. It stays as organized materials rather than a full course order.
Not included here
25 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (25 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Readings
- Notes on the level set method Download
- Presentation on the level set method (Courtesy of Per Olof Persson. Used with permission.) Download
Lecture Notes
24 files
- Lecture 1 · Fundamental concepts and examples · Files Download
- Lecture 2 · Well-posedness and Fourier methods for linear initial value problems · Files Download
- Lecture 3 · Laplace and Poisson equation · Files Download
- Lecture 4 · Heat equation, transport equation, wave equation · Files Download
- Lecture 5 · General finite difference approach and Poisson equation · Files Download
- Lecture 6 · Elliptic equations and errors, stability, Lax equivalence theorem · Files Download
- Lecture 7 · Spectral methods · Files Download
- Lecture 9 · Spectral methods · Files Download
- Lecture 10 · Elliptic equations and linear systems · Files Download
- Lecture 11 · Efficient methods for sparse linear systems: Multigrid · Files Download
- Lecture 12 · Efficient methods for sparse linear systems: Krylov methods · Files Download
- Lecture 13 · Ordinary differential equations · Files Download
- Lecture 14 · Stability for ODE and von Neumann stability analysis · Files Download
- Lecture 15 · Advection equation and modified equation · Files Download
- Lecture 16 · Advection equation and ENO/WENO · Files Download
- Lecture 17 · Conservation laws: Theory · Files Download
- Lecture 18 · Conservation laws: Numerical methods · Files Download
- Lecture 19 · Conservation laws: High resolution methods · Files Download
- Lecture 20 · Operator splitting, fractional steps · Files Download
- Lecture 21 · Systems of IVP, wave equation, leapfrog, staggered grids · Files Download
- Lecture 22 · Level set method · Files Download
- Lecture 23 · Navier-Stokes equation: Finite difference methods · Files Download
- Lecture 24 · Navier-Stokes equation: Pseudospectral methods · Files Download
- Lecture 25 · Particle methods · Files Download
Assignments
MATLAB Files
- Four linear PDE solved by Fourier series: mit18086_linpde_fourier.m Download
- Compute stencil approximating a derivative given a set of points and plot von Neumann growth factor: mit18086_stencil_stability.m Download
- Error convergence for the 1d Poisson equation: mit18336_poisson1d_error.m Download
- Demo for elimination with reordering: moe.m Download
Other materials from this course
Course outline
Lecture Notes · Lecture Notes
Lecture 2: Well-posedness and Fourier methods for linear initial value problems
Lecture Notes · Lecture Notes
Lecture 3: Laplace and Poisson equation
Lecture Notes · Lecture Notes
Lecture 4: Heat equation, transport equation, wave equation
Lecture Notes · Lecture Notes
Lecture 5: General finite difference approach and Poisson equation
Lecture Notes · Lecture Notes
Lecture 6: Elliptic equations and errors, stability, Lax equivalence theorem
Lecture Notes · Lecture Notes
Lecture 7: Spectral methods
Lecture Notes · Lecture Notes
Lecture 8: Fast Fourier transform (guest lecture by Steven Johnson)
Lecture Notes · Lecture Notes
Lecture 9: Spectral methods
Lecture Notes · Lecture Notes
Lecture 10: Elliptic equations and linear systems
Lecture Notes · Lecture Notes
Lecture 11: Efficient methods for sparse linear systems: Multigrid
Lecture Notes · Lecture Notes
Lecture 12: Efficient methods for sparse linear systems: Krylov methods
Lecture Notes · Lecture Notes
Lecture 13: Ordinary differential equations
Lecture Notes · Lecture Notes
Lecture 14: Stability for ODE and von Neumann stability analysis
Lecture Notes · Lecture Notes
Lecture 15: Advection equation and modified equation
Lecture Notes · Lecture Notes
Lecture 16: Advection equation and ENO/WENO
Lecture Notes · Lecture Notes
Lecture 17: Conservation laws: Theory
Lecture Notes · Lecture Notes
Lecture 18: Conservation laws: Numerical methods
Lecture Notes · Lecture Notes
Lecture 19: Conservation laws: High resolution methods
Lecture Notes · Lecture Notes
Lecture 20: Operator splitting, fractional steps
Lecture Notes · Lecture Notes
Lecture 21: Systems of IVP, wave equation, leapfrog, staggered grids
Lecture Notes · Lecture Notes
Lecture 22: Level set method
Lecture Notes · Lecture Notes
Lecture 23: Navier-Stokes equation: Finite difference methods
Lecture Notes · Lecture Notes
Lecture 24: Navier-Stokes equation: Pseudospectral methods
Lecture Notes · Lecture Notes
Lecture 25: Particle methods
Lecture Notes · Lecture Notes
Lecture 26: Project presentations
MIT OpenCourseWare, Dr. Benjamin Seibold, 18.336 Numerical Methods for Partial Differential Equations, Spring 2009.
License: CC BY-NC-SA 4.0 · Edition: Spring 2009 · Open the original course on OCW ↗
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