Christopherson was born the son of a clergyman, Derman Christopherson (the vicar of Plumstead in southeast London), and Edith Frances Christopherson. Soon afterwards, the Christopherson family moved to Porlock in Devon, where his father was vicar of Clovelly. As a boy, Christopherson suffered from asthma. He was educated privately until, at age 14, he was sent to Sherborne School in Dorset.
Christopherson was the first to apply the method in the solution of field differential equations, which later became the most important application. He gained his DPhil in 1941.
Christopherson married Frances Edith Tearle in 1940; the couple had five children. Their son, Peter Christopherson (1955-2010), was a musician, video director and designer. Lady Christopherson predeceased her husband in 1988.