Finite Differences, Accuracy, Stability, Convergence

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

Course Lectures

• Difference Methods for Ordinary Differential Equations

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Finite Differences, Accuracy, Stability, Convergence

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• The One-way Wave Equation and CFL / von Neumann Stability

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Comparison of Methods for the Wave Equation

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Second-order Wave Equation (including leapfrog)

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Wave Profiles, Heat Equation / Point Source

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Finite Differences for the Heat Equation

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Convection-Diffusion / Conservation Laws

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Conservation Laws / Analysis / Shocks

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Shocks and Fans from Point Source

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Level Set Method

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Matrices in Difference Equations (1D, 2D, 3D)

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Elimination with Reordering: Sparse Matrices

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Financial Mathematics / Black-Scholes Equation

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Iterative Methods and Preconditioners

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• General Methods for Sparse Systems

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Multigrid Methods

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Krylov Methods / Multigrid Continued

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Conjugate Gradient Method

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Fast Poisson Solver

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Optimization with constraints

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Weighted Least Squares

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Calculus of Variations / Weak Form

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Error Estimates / Projections

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Saddle Points / Inf-sup condition

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Two Squares / Equality Constraint Bu = d

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Regularization by Penalty Term

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Linear Programming and Duality

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Duality Puzzle / Inverse Problem / Integral Equations

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.