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- Jim Douglas, Chieh-Sen Huang, Felipe Pereira
- Numerische Mathematik
- 1999

The MMOC procedure for approximating the solutions of transport-dominated diiusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of ow problems. The variant, called the MMOCAA, discussed herein preserves the conservation law at a minor additional computational cost. It is shown that itsâ€¦ (More)

- Jim Douglas, Seongjai Kim
- 2001

Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time stepping procedure such as Crank-Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time stepping procedure. We show that minor modi cationsâ€¦ (More)

- Jim Douglas
- Proceedings of the National Academy of Sciencesâ€¦
- 1951

We present a new, naturally parallelizable, accurate numerical method for the solution of transport-dominated diffusion processes in heterogeneous porous media. For the discretization in time of one of the governing partial differential equations, we introduce a new characteristics-based procedure which is mass conservative, the modified method ofâ€¦ (More)

- Jim Douglas, Seongjai Kim
- 1999

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematicalâ€¦ (More)

- Jim Douglas, James E. Gunn
- J. ACM
- 1962

A is constant and positive definite, and where the boundary values of ~ are specified on the faces of a rectangular parallelepiped in Cartesian m-space. The linear case will be t reated first, and second-order accuracy in both space and time will be demonstrated without restrictions involving the space and time increments. The nonlinear case will then beâ€¦ (More)

We introduce an accurate and efficient alternating-direction method for solving a viscous wave equation which is based on a three-level, second-order correct implicit algorithm and which has a splitting error not significantly larger than the truncation error of the base method.

This article is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave equations. A three-level second-order implicit algorithm is considered without introducing auxiliary variables. As a perturbation of the algorithm, a locally one-dimensional (LOD) procedure which has a splitting error not larger than theâ€¦ (More)

- Jim Douglas
- Proceedings of the National Academy of Sciencesâ€¦
- 1951