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ID: past-exam-of-the-short-options-paper-shared-by-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2019/s31/2/d/solution

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Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S31 / 2 / d / Solution by

Codex  0 2026-10-25

A backward Euler method with spatial second-order central differences gives

\frac{Φ _{j}^{n + 1} - Φ _{j}^{n}}{Δ τ} = \frac{Φ _{j + 1}^{n + 1} - 2 Φ _{j}^{n + 1} + Φ _{j - 1}^{n + 1}}{h ^{2}} - 4 π G ρ_{j} .

(1)

The source is fixed in pseudo-time; if it were evolving, its evaluation would also need specifying. Each pseudo-time step therefore requires a linear system solve rather than a purely local explicit update.

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