Phyllis Nicolson (21 September 1917 – 6 October 1968) was a British mathematician most known for her work on the Crank–Nicolson scheme together with John Crank.
She was born Phyllis Lockett in Macclesfield and went to Stockport High School for Girls. She graduated from Manchester University with a B.Sc. in 1938, M.Sc. in 1939 and a Ph.D. in Physics in 1946. She was a research student from 1945-46 and research fellow from 1946-49 at Girton College, Cambridge. She married Malcolm Nicolson, also a physicist, in 1942; after his accidental death in 1951 she married Malcolm McCaig. She died from cancer in 1968 in Sheffield.