Alternating direction iteration for mildly nonlinear elliptic difference equations

The Numerical Solution of Parabolic and Elliptic Differential Equations

D.W. Peaceman, H.H. Rachford · Journal of the Society for Industrial and Applied Mathematics · 1955 · 3.3K citations

Natural Sciences, Computational Engineering, Physics +17

On the numerical solution of heat conduction problems in two and three space variables

Jim Douglas, H.H. Rachford · Transactions of the American Mathematical Society · 1956 · 1.7K citations

Engineering, Mechanical Engineering, Computational Heat Transfer +6

Iterative methods for solving partial difference equations of elliptic type

David M. Young · Transactions of the American Mathematical Society · 1954 · 695 citations · Full text

Computing, Computer Science, Computational Mechanics +11

<i>Methods of Mathematical Physics, Vol. I</i>

Richard Courant, David Hilbert · Physics Today · 1954 · 540 citations

Natural Sciences, Mathematics, Physics +12

On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods

Jim Douglas · Journal of the Society for Industrial and Applied Mathematics · 1955 · 285 citations

Natural Sciences, Mathematics, Petroleum Engineering +16