A Comparison of Some Numerical Methods for Solving Volterra Integral Equations.

Identifier

95

Author

Scotty Glen Houston

Date

2010

Document Type

Thesis

Degree Name

Master of Science

Major

Mathematical Sciences

Concentration

Applied Mathematics

Committee Chair

Alistair James Windsor

Committee Member

John R Haddock

Committee Member

Maria Fernanda Botelho

Abstract

We implement several methods for solving Volterra integral equations based on standard techniques for solving ordinary differential equations. In particularwe implement a version of the modified Euler method,we implement the standard fourth order Runge-Kutta method.We compare these with a novel collocation method using Bernstein polynomials.We also look at Volterra integral equations with weakly singular kernels. Here the standard methods developed above do not apply though the collocation method can still be used. We develop two “product integration” methods, derived from numerical integration methods that can be applied to these weakly singular Volterra integral equations and compare them to the collocation method.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

Recommended Citation

Houston, Scotty Glen, "A Comparison of Some Numerical Methods for Solving Volterra Integral Equations." (2010). Electronic Theses and Dissertations. 61.
https://digitalcommons.memphis.edu/etd/61