Jeremiah Hampton |
Home Institution: University of Mississippi
Discipline: Electrical Engineering Mentor’s Name: Dr. Richard Gordon Expected Graduation Date: May 2007 List of Organizations and Honors:
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ABSTRACT
Radial Basis Functions: Numerical Method for Solving Partial Differential Equations
| Radial Basis Functions (RBF) has become one of the most important scientific
topics over the last several years. They have been used heavily in
the area of civil engineering, specifically in the field of neural networks
because they have great interpolation qualities. Even though the
use of radial basis functions as a solution for Partial Differential Equations
(PDE) is very effective, it is very time-consuming and complicated.
The problems stated above are what led to this research. In this
paper, radial basis functions are used in a meshless method to solve partial
differential equation. Also, a Fortran computer program will be used
to try and solve the partial differential equations (PDE) with accuracy
and efficiency. Several examples will be presented and some of the
advantages and disadvantages of the proposed methods will be discussed.
Here are some of the key words used throughout the research paper:
1. Radial Basis Functions (RBF) - A set of powerful functions that are used to approximate scattered data in several dimensions. 2. Partial Differential Equations (PDE)– Equations that can be used to explain and create advancements in modern technology. 3. Meshless Method – A method were no connection has to be known
between the neighboring data points or nodes.
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