Biography

(1934

38)

(1953)

1945

1957

(

)

1957

1981

1940

u ( x , t ) u(x, t) u ( x , t )

u t − u x x = 0 u_{t} - u_{xx} = 0 u t ​ − u x x ​ = 0

t > 0 t > 0 t > 0

u ( x , 0 ) = f ( x ) u(x, 0) = f (x) u ( x , 0 ) = f ( x )

x x x

x x x

t t t

u t ( x , t ) u_{t}(x, t) u t ​ ( x , t )

u x x ( x , t ) u_{xx}(x, t) u x x ​ ( x , t )

1910

(

)

was a student of Lawrence Bragg and Douglas Hartree at Manchester University, where he was awarded the degrees of B.Sc. and M.Sc. and laterD.Sc. After war work on ballistics he was a mathematical physicist at Courtaulds Fundamental Research Laboratory fromtoand professor of mathematics at Brunel Universityinitially Brunel College in Actonfromto. His main work was on the numerical solution of partial differential equations and, in particular, the solution of heat-conduction problems. In thes such calculations were carried out on simple mechanical desk machines. Crank is quoted as saying that to "burn a piece of wood" numerically then could take a week.John Crank is best known for his joint work with Phyllis Nicolson on the heat equation, where a continuous solutionis required which satisfies the second order partial differential equationfor, subject to an initial condition of the formfor all real. They considered numerical methods which find an approximate solution on a grid of values ofand, replacingandby finite difference approximations. One of the simplest such replacements was proposed by L F Richardson in Richardson 's method yielded a numerical solution which was very easy to compute, but alas was numerically unstable and thus useless. The instability was not recognised until lengthy numerical computations were carried out by Crank, Nicolson and others. Crank and Nicolson 's method, which is numerically stable, requires the solution of a very simple system of linear equationsa tridiagonal systemat each time level.