Dr. Leigh C. Becker: New Applications

Constant Delay Differential Equations and the Method of Steps

Dr. Leigh Becker — Mon, 08 Jun 2009 04:00:00 Z

A Maple procedure for the "method of steps" is defined that can be used to compute solutions of the scalar linear delay differential equation

with constant delay , where and are continuous functions for . Five examples illustrate the procedure.

Scalar Volterra Integro-Differential Equations

Dr. Leigh Becker — Wed, 22 Aug 2007 00:00:00 Z

This worksheet can be used as an experimental tool to investigate the general behavior of solutions of scalar Volterra integro-differential equations of the form z'(t) = a(t) z(t) + int(b(t, s, z(s)), s = 0 .. t) + g(t) by numerically solving them with the implicit trapezoidal rule and Newton's method for nonlinear systems---and then graphing their solutions.

Numerical and Graphical Solutions of Volterra Integral Equations of the Second Kind

Dr. Leigh Becker — Thu, 09 Jun 2005 00:00:00 Z

The Maple procedure in this worksheet employs the implicit trapezoidal rule in conjunction with Newton's method for nonlinear systems to compute and graph numerical solutions of systems of Volterra integral equations of the second kind. There are four examples to illustrate the use of the procedure. Numerical solutions of scalar Volterra integro-differential equations can also be computed and graphed by modifying one of the examples.