Welcome to Maths 26th May 2020
In this historical feature we explore Phyllis Nicolson (1917-1968) and her influential work.
Phyllis Nicolson (née Lockett), most well-known for her work on the Crank-Nicolson method, received her BSc (1938), MSc (1939) and PhD (1946) in Physics from the University of Manchester before taking up a research fellowship at Cambridge University for three years. After the accidental death of her husband in 1952, she was appointed to take over his lectureship in Physics at Leeds University.
Between 1940 and 1945, Nicolson was part of a research group at the University of Manchester led by Douglas Hartree (famous for the Hartee-Fock method) which worked on wartime problems for the Ministry of Supply, one being magnetron theory and performance.
With John Crank, Phyllis worked on a method to numerically solve the heat equation and other similar partial differential equations. The Crank-Nicolson method improved on previous methods such as the one put forward by Lewis Fry Richardson in 1910. Richardson’s method made it possible to easily compute a numerical solution for the heat equation but it was numerically unstable. The Crank-Nicolson method, which is numerically stable, is based on the trapezoidal rule which requires solutions to simple linear equations at each time step.
Phyllis died of breast cancer in 1968 at the age of 51.