# Phyllis Nicolson

### Quick Info

Born
21 September 1917
Macclesfield, England
Died
6 October 1968
Sheffield, England

Summary
Phyllis Nicolson was an English mathematician best known for her work in numerical analysis.

### Biography

Phyllis Nicolson's maiden name was Lockett. She was educated at Stockport High School and received the degrees of B.Sc. (1938) and M.Sc. (1939) and Ph.D. in Physics (1946) from Manchester University and was a research student (1945-46) and research fellow (1946-49) at Girton College, Cambridge. In 1942 she married Malcolm Nicolson. She had a strong wish to have her first child before reaching thirty, and she achieved this ambition with a day to spare. After her husband's untimely death in a train crash in 1952, she was appointed to fill his lectureship in Physics at Leeds University. In 1955 she married Malcolm McCaig, who was also a physicist.

During the period 1940-45 she was a member of a research group in Manchester University directed by Douglas Hartree, working on wartime problems for the Ministry of Supply, one being concerned with magnetron theory and performance. Phyllis Nicolson is best known for her joint work with John Crank on the heat equation, where a continuous solution $u(x, t)$ is required which satisfies the second order partial differential equation
$u_{t} - u_{xx} = 0$
for $t > 0$, subject to an initial condition of the form $u(x, 0) = f (x)$ for all real $x$. They considered numerical methods which find an approximate solution on a grid of values of $x$ and $t$, replacing $u_{t}(x, t)$ and $u_{xx}(x, t)$ by finite difference approximations. One of the simplest such replacements was proposed by L F Richardson in 1910. Richardson's method yielded a numerical solution which was very easy to compute, but alas was numerically unstable and thus useless. The instability was not recognised until lengthy numerical computations were carried out by Crank, Nicolson and others. Crank and Nicolson's method, which is numerically stable, requires the solution of a very simple system of linear equations (a tridiagonal system) at each time level.

Nicolson died of breast cancer in 1968

### References (show)

1. J Crank and P Nicolson. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Cambridge Philos. Soc. 43 (1947). 50-67. [Re-published in: John Crank 80th birthday special issue Adv. Comput. Math. 6 (1997) 207-226]
2. E Isaacson and H B Keller, Analysis of Numerical Methods (New York, 1966).