NDLI: Analog Computation of Green's Function for Integrating Two-Point Boundary Value Problems

Content Provider	IEEE Xplore Digital Library
Author	Terasaki, Richard M.
Copyright Year	1955
Abstract	A method is described for the analog computation of the solution of linear two-point boundary value problems, i.e., the problem of a linear ordinary differential equation with linear two-point boundary conditions. The nonhomogeneous problem, in particular, is considered; the differential equal for y on the real interval 0¿x¿1 is taken to be nonhomogeneous. The method for its solution is based upon the integral formula for the solution, namely, y(x) = ¿01G(x, t)f(t)dt, where G(x,t) is the Green's function satisfying two-point boundary conditions while f is a known integrable function. The paper describes a method for finding a specific set of initial value problems whose solutions, taken in linear combination, form the Green's function whose second argument (t) is fixed. This technique reduces the two-point boundary value problem to a set of initial value types and makes the continuous computation of the Green's function as a function of x for fixed t amenable to analog means. The application of the described technique to the adjoint boundary value problem yields a means for continuous computation of G as a function of the second argument (t) for fixed values of the first argument (x). This is the required form for the analog evaluation of the integral formula. The theoretical aspects of the method found are stated, after which an example of a simple non-self-adjoint problem from the study of structures is solved on an electronic analog computer.
Starting Page	57
Ending Page	63
Page Count	7
File Size	1115701
File Format	PDF
ISSN	03679950
Volume Number	EC-11
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1962-02-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Analog computers Green's function methods Boundary value problems Water heating Temperature Aircraft Insulation Computational modeling Differential equations Boundary conditions
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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