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1.5 Computer quiz

  1. Do you have to register to study this course on-line?
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  2. The equation $ \partial_{xxx}f -\partial_{xx}f\sqrt{1+(\partial_x f)^2}=\sin(xf)$ with $ f(0)=0$ , $ f^\prime(0)=1$
    1. is an ODE that can be solved for example with the Runge-Kutta method
    2. is an ODE that can only be solved only with an extra condition f(1)=0
    3. is a third order PDE that cannot be solved with a Runge-Kutta method

  3. The equation $ 2\partial_{tt}f -2\partial_{xt}f +2\partial_{xx}f=0$ has
    1. 2 characteristics, i.e. solutions that propagate like waves
    2. 1 characteristics, i.e. solutions that propagate like heat pulses
    3. 0 characteristics, i.e. solutions that do no propagate

  4. When a heat pulse hits the edge of a perfectly insulated domain
    1. it leaves the domain while satisfying the Neuman boundary conditions
    2. it stops and reaches kind of a steady state
    3. it gets reflected and propagates backward inside the domain

  5. Advection/diffusion are not uniquely defined in an inhomogeneous medium $ D=D(x)$
    1. true: a diffusion coefficient gradient has the same effect as an advection
    2. false: advection and diffusion are always uniquely defined

  6. Successive doubling of the numerical resolution yields values 1.03, 2.98, 4.01, 4.50 that
    1. converge like the square-root to a value around 6
    2. converge linearly to a value around 5
    3. converge quadratically to a value around 5
    4. do not seem to converge

  7. To approximate a Gaussian $ \exp(-x^2), x\in[-3; 3]$ with 1% accuracy you need
    1. approx 100 linear FEM
    2. approx 1000 linear FEM
    3. approx 100 particles
    4. approx 10000 particles

SYLLABUS  Previous: 1.4.7 Sampling with quasi-particles  Up: 1 INTRODUCTION  Next: 1.6 Exercises