Dr. Leigh C. Becker: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=9148
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 06 May 2016 03:41:52 GMTFri, 06 May 2016 03:41:52 GMTNew applications published by Dr. Leigh C. Beckerhttp://www.mapleprimes.com/images/mapleapps.gifDr. Leigh C. Becker: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=9148
Constant Delay Differential Equations and the Method of Steps
http://www.maplesoft.com/applications/view.aspx?SID=33093&ref=Feed
<p>A Maple procedure for the "method of steps" is defined that can be used to compute solutions of the scalar linear delay differential equation</p>
<p align="center"><img align="absmiddle" alt="diff(x(t), t) = a(t)*x(t)+b(t)*x(t-h)" src="http://maplenet.maplesoft.com/maplenet/primes/32AADE52534CB62D8571A38E92E91AB4.gif" /></p>
<p>with constant delay <img align="absmiddle" alt="h > 0" src="" />, where <img align="absmiddle" alt="a(t)" src="http://maplenet.maplesoft.com/maplenet/primes/0ED99DC3928F0D1F38325BE5A6744563.gif" /> and <img align="absmiddle" alt="b(t)" src="http://maplenet.maplesoft.com/maplenet/primes/1FD489AA0AC13F1FB970F4DBF0192035.gif" /> are continuous functions for <img align="absmiddle" alt="t >= 0" src="" />. Five examples illustrate the procedure.</p><img src="/view.aspx?si=33093/VariableCoeffs.gif" alt="Constant Delay Differential Equations and the Method of Steps" align="left"/><p>A Maple procedure for the "method of steps" is defined that can be used to compute solutions of the scalar linear delay differential equation</p>
<p align="center"><img align="absmiddle" alt="diff(x(t), t) = a(t)*x(t)+b(t)*x(t-h)" src="http://maplenet.maplesoft.com/maplenet/primes/32AADE52534CB62D8571A38E92E91AB4.gif" /></p>
<p>with constant delay <img align="absmiddle" alt="h > 0" src="" />, where <img align="absmiddle" alt="a(t)" src="http://maplenet.maplesoft.com/maplenet/primes/0ED99DC3928F0D1F38325BE5A6744563.gif" /> and <img align="absmiddle" alt="b(t)" src="http://maplenet.maplesoft.com/maplenet/primes/1FD489AA0AC13F1FB970F4DBF0192035.gif" /> are continuous functions for <img align="absmiddle" alt="t >= 0" src="" />. Five examples illustrate the procedure.</p>33093Mon, 08 Jun 2009 04:00:00 ZDr. Leigh BeckerDr. Leigh BeckerScalar Volterra Integro-Differential Equations
http://www.maplesoft.com/applications/view.aspx?SID=5148&ref=Feed
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.<img src="/view.aspx?si=5148/IntegroDE_209.jpg" alt="Scalar Volterra Integro-Differential Equations" align="left"/>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.5148Wed, 22 Aug 2007 00:00:00 ZDr. Leigh BeckerDr. Leigh BeckerNumerical and Graphical Solutions of Volterra Integral Equations of the Second Kind
http://www.maplesoft.com/applications/view.aspx?SID=1622&ref=Feed
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.<img src="/view.aspx?si=1622/Volterra_120.gif" alt="Numerical and Graphical Solutions of Volterra Integral Equations of the Second Kind" align="left"/>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.1622Thu, 09 Jun 2005 00:00:00 ZDr. Leigh BeckerDr. Leigh Becker