By the time he went to Brunel in 1957 he was already a recognised expert in the numerical solution of partial differential equations, particularly the heat equation, which stretches back two centuries to JBJ Fourier, one of Napoleon's mathematicians.
In the 1940s the calculations required to solve this, the most common of partial differential equations, were carried out on simple mechanical desk machines, and required an enormous amount of the most exacting work. Crank said that to "burn a piece of wood numerically" in those days -- without computers -- could take a week.
His work with Phyllis Nicolson, a near contemporary of his as a student at Manchester University, on the numerical solution of the heat equation sprang from a method for solving this problem which had been proposed by LF Richardson in 1910.
Richardson's method yielded a numerical solution which was very easy to compute, but which was numerically unstable Ñ and thus useless. The instability was not recognised until lengthy numerical computations were carried out by Crank, Nicolson, and others. Crank and Nicolson devised a method which is numerically stable and which turned out to be so fundamental and useful that it is a cornerstone of every discussion of the numerical solution of partial differential equations.
Since its inception, it has been used routinely in computer codes, with applications ranging from options pricing and oceanography to pattern formation and petrology.
John Crank was born on February 6 1916 at Hindley, Lancashire, the only son of a carpenter's pattern-maker. He studied at Manchester University, where he gained his BSc and MSc. At Manchester he was a student of the physicist Lawrence Bragg, the youngest-ever winner of a Nobel prize, and of Douglas Hartree, a leading numerical analyst.
Crank was seconded to war work during the Second World War, in his case to work on ballistics. This was followed by employment as a mathematical physicist at Courtaulds Fundamental Research Laboratory from 1945 to 1957. He was then, from 1957 to 1981, professor of mathematics at Brunel University (initially Brunel College in Acton).
Crank published only a few research papers, but they were seminal. Even more influential were his books. His work at Courtaulds led him to write The Mathematics of Diffusion, a much-cited text that is still an inspiration for researchers who strive to understand how heat and mass can be transferred in crystalline and polymeric material. He subsequently produced Free and Moving Boundary Problems, which encompassed the analysis and numerical solution of a class of mathematical models that are fundamental to industrial processes such as crystal growth and food refrigeration.
As a specialist in numerical mathematics, Crank was a figure of particular importance at a time when that area was often regarded by the mathematical establishment as being rather slight, and he attracted a cadre of devoted students and young collaborators. He was a founder member of the Institute of Mathematics and its Applications, and a key player in the setting up of the Royal Institution Mathematics programme.
Crank was a fine raconteur and a good listener, with a kindly sense of humour, admired and respected by his colleagues and loved by his many students.
He met his wife, Joan, to whom he was married for 63 years, on a Holiday Fellowship walking holiday. They retained an enthusiasm for walking and were also keen gardeners.
His retirement gift to Brunel was a garden; and recently the university named a building after him. Joan Crank died in 2005; he is survived by their two children.