Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 41E / c

Table of contents
- Solution c

Solution

For the same Fourier mode, the leapfrog finite-difference scheme for the diffusion equation gives

r^{n + 1} = r^{n - 1} - 2 q r^{n}, p (r) = r^{2} + 2 q r - 1.

The two amplification roots are

r_{\pm} = - q \pm 1 + q^{2} .

For every nonzero mode

q > 0

, one has

∣ r_{-} ∣ = q + 1 + q^{2} > 1.

Thus every

μ > 0

admits a growing Fourier mode, and

the leapfrog scheme is unstable for every μ > 0.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version