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nonlinear dynamics

Scientific Computing for DPhil Students
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PDEs (5.8)

In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
Scientific Computing for DPhil Students
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PDEs (5.7)

In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.
Scientific Computing for DPhil Students
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PDEs (5.6)

In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
Scientific Computing for DPhil Students
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PDEs (5.5)

In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
Scientific Computing for DPhil Students
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PDEs (5.4)

In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
Scientific Computing for DPhil Students
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PDEs (5.3)

In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs.
Scientific Computing for DPhil Students
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PDEs (5.2)

In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
Scientific Computing for DPhil Students
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PDEs (5.1)

In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
Scientific Computing for DPhil Students
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ODEs and Nonlinear Dynamics (4.4)

In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
Scientific Computing for DPhil Students
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ODEs and Nonlinear Dynamics (4.3)

In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100-digit challenge.
Scientific Computing for DPhil Students
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ODEs and Nonlinear Dynamics (4.2)

In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
Scientific Computing for DPhil Students
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ODEs and Nonlinear Dynamics (4.1)

In this lecture, Professor Trefethen discusses ODEs and IVPs, Runge-Kutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun.

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