**Time-Split Methods for Partial Differential Equations.
**

by Randall J. LeVeque. PhD Dissertation, Stanford University, 1982.

**Abstract.**
This thesis concerns the use of time-split methods for the
numerical solution of time-dependent partial differential equations.
Frequently the differential operator splits additively into two or more
pieces such that the corresponding subproblems are each easier to solve than
the original equation, or are best handled by different techniques. In the
time-split method the solution to the original equation is advanced by
alternately solving the subproblems. In this thesis a unified approach to
splitting methods is developed which simplifies their analysis. Particular
emphasis is given to splittings of hyperbolic problems into subproblems with
disparate wave speeds. Three main aspects of the method are considered. The
first is the accuracy and efficiency of the time-split method relative to
unsplit methods. The second topic is stability for split methods. The final
topic is the proper specification of boundary data for the intermediate
solutions, e.g., the solution obtained after solving only one of the
subproblems. The main emphasis is on hyperbolic problems, and the
one-dimensional shallow water equations are used as a specific example
throughout. The final chapter is devoted to some other applications or the
theory. Two-dimensional hyperbolic problems, convection-diffusion equations,
and the Peaceman-Rachford ADI method for the heat equation are considered.

**Keywords.**
*Partial differential equations, *Time dependence,
*Splitting, *Numerical methods and procedures, *Solutions(General), Accuracy,
Efficiency, Stability, Boundary value problems, Hyperbolas, Cauchy problem,
Operators(Mathematics), Two dimensional, One dimensional, Shallow water,
Waves, Velocity, Theses

**pdf file:**
ADA119417.pdf
From: Defense
Technical Information Center, ADA 119417

**bibtex entry:**

@phdthesis{leveque:phd, Author = {R. J. {LeVeque}}, School = {Stanford University}, Title = {Time-split methods for partial differential equations}, Year = {1982}}