5. Partial Differential Equations

Time Integration — Quiz

Test your understanding of time integration with 5 practice questions.

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Practice Questions

Question 1

According to the Dahlquist barrier, what is the maximum order that an A-stable linear multistep method can achieve?

Question 2

What is the method-of-lines approach in solving time-dependent PDEs?

Question 3

Which stability function R(z) corresponds to Heun’s explicit trapezoidal method applied to $y'=\lambda y$?

Question 4

For the two-dimensional diffusion equation $u_t=\alpha(u_{xx}+u_{yy})$, discretized with explicit FTCS on a uniform grid with $\Delta x=\Delta y$, what is the stability condition on $\Delta t$ in terms of $\alpha$ and $\Delta x$?

Question 5

In the one-step $\theta$-method for $y'=\lambda y$, for which values of $\theta$ is the method A-stable?