Phyllis Nicolson (21 September 1917 – 6 October 1968) was a British mathematician and physicist best known for her work on the Crank–Nicolson method together with John Crank.

[3] Nicolson's Ph.D. was expected to be submitted in 1941 but was interrupted by wartime work with Douglas Hartree's research group at Manchester University from 1940 to 1945.

During this time, Nicolson became a proficient numerical analyst and an expert user of Hartree's differential analyser.

Nicolson's two significant bodies of wartime research, "Transient behaviour in the single anode magnetron" and "heat conduction", formed the basis of parts II and III of her 1946 PhD thesis Three Problems in Theoretical Physics.

[6] Malcolm Nicolson, aged 33, died in a train accident in December 1951, and Phyllis was appointed to take over his lectureship.