This course addresses graduate students of all fields who are interested in numerical methods for partial differential equations. Many modern and efficient approaches are presented, after fundamentals of numerical approximation are established. It particularly focus on a qualitative understanding of the considered partial differential equation, fundamentals of finite difference, finite volume, finite element, and spectral methods, and important concepts such as stability.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|Fundamental concepts and examples||00:05:00|
|Well-posedness and Fourier methods for linear initial value problems||00:05:00|
|Laplace and Poisson equation||00:05:00|
|Heat equation, transport equation, wave equation||00:05:00|
|General finite difference approach and Poisson equation||00:10:00|
|Elliptic equations and errors, stability, Lax equivalence theorem||00:05:00|
|Spectral methods Part 2||00:10:00|
|Elliptic equations and linear systems||00:05:00|
|Efficient methods for sparse linear systems Multigrid||00:10:00|
|Efficient methods for sparse linear systems Krylov methods||00:05:00|
|Ordinary differential equations||00:05:00|
|Stability for ODE and von Neumann stability analysis||00:05:00|
|Advection equation and modified equation||00:05:00|
|Advection equation and ENO/WENO||00:10:00|
|Conservation laws Theory||00:05:00|
|Conservation laws Numerical methods||00:05:00|
|Conservation laws High resolution methods||00:10:00|
|Operator splitting, fractional steps||00:05:00|
|Systems of IVP, wave equation, leapfrog, staggered grids||00:05:00|
|Level set method||00:05:00|
|Navier-Stokes equation Finite difference methods||00:05:00|
|Navier-Stokes equation Pseudospectral methods||00:05:00|
|Submit Your Assignment||00:00:00|
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