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Innovation

# Green's Function Computation

University of Santiago de Compostela
posted on 05/08/2012

The developed software, which run in Mahematica, provides a tool for calculating the explicit expression of the Green’s function related to a nth – order linear ordinary differential equation, with constant coefficients, coupled with two – point linear boundary conditions. It offers the graphical and analytical solution of the system of equations. The computation of Green’s functions have a great interest in fields such as quantum mechanics, electrodynamics, nanoelectronics, etc. The software has been developed as a collaboration between researches of the University of Santiago de Compostela and the University of Vigo.

Suggested Uses

Compute solutions of system involving Green's Functions, such as electrodymanics, quantum mechanics, nanoelectronics, etc.

To the best of our knowledge it is the first software available to compute the Green’s function in an easy way and with a friendly format.

Innovation Details

Detailed Description

This software calculates the Green’s function, G(t,s), from the boundary value problem given by a linear nth - order ODE with constant coefficients:

u(n)(t)+c1u(n-1)(t)+c2u(n-2)(t)...cnu(t) t ∈[a,b]

together with the boudnary conditions:

n-1 j=0 αiju(j)(a)+ βiju(j)(b)

This Mathematica package provides a tool valid for calculating the explicit expression of the Green’s function related to a nth – order linear ordinary differential equation, with constant coefficients, coupled with two – point linear boundary conditions.
The system allows to configure the following parameters:

• Order: the order of the differential equation (natural number)
• Coefficients: coefficients vector of the differential equation {c1, ... cn}. The system allows to introduce parameters, but in this case the solution will be only analytical and not graphical.
• Endpoints of the interval (a and b)
• Periodic conditions: enables the use of periodic boundary conditions.
• Boundary conditions: a vector containing the boundary conditions.

File Number: 13

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Case Manager:

 Fernando Pardo Innovations (31)

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February 11, 2009

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