Third Order Difference Methods for Hyperbolic Equations

Technical Report · Mon Dec 01 00:00:00 EST 1969

DOI:https://doi.org/10.2172/4173236· OSTI ID:4173236

Burstein, Samuel Z. ^[1]; Mirin, Arthur ^[1]

---

1. New York Univ. (NYU), NY (United States)

In recent years there has appeared in the literature a surge in the number of papers dealing with numerical solutions of partial differential equations. And, usually, the difference methods employed are of first or second order of accuracy. This restriction is not an arbitrary one, but rather, is related to the fact that computing machines have been relatively slow and their high speed memory capacity has been small; hence a usable computational scheme must necessarily have the attribute of simplicity. In problems of more than one space dimension, even greater emphasis is placed on simplicity. It is anticipated, however, that a new era of computability is almost upon us. We are referring to the use of parallel processors, i.e. N-serial type computing processors, each of which is synchronized and each of which can communicate with the other processors through a common memory or central controller. The value of N may be from 2⁶ to 2⁸ and the arithmetic speed of each individual processing unit will be in the sub-microsecond range. By proper organizing of the data, each mesh point or string of mesh points may have its own central processor, which means the solution on the entire mesh may be advanced essentially simultaneously. For such a class of computing machines the requirement of simplicity for the difference scheme may be relaxed. In this note, we propose a class of difference schemes for hyperbolic problems in one and two space dimensions. The methods are applicable to nonlinear initial value problems; they are uniformly third order accurate on both the space variables and time and are similar to methods proposed by Strang.

• Research Organization: New York Univ. (NYU), NY (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• NSA Number: NSA-24-016371
• OSTI ID: 4173236
• Report Number(s): NYO--1480-136
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
DIFFERENTIAL EQUATIONS
N32000* --Physics (General)
differential equations/third order difference methods for hyperbolic