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Solution of some partial differential equations using State space techniques

✍ Scribed by Curtis W. Dodd; Someshwar C. Gupta

Publisher: Elsevier Science
Year: 1969
Tongue: English
Weight: 730 KB
Volume: 287
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(69)90003-9

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✦ Synopsis

The spatial discretization technique for the solution of certain partial differential equatio>ls is discussed. After determining a valid mathematical representation for the canonical parabolic partial differential equation two methods of determining the stability of the resulting high order system of ordinary dQferentia1 equations is presented. Next the solutio)z to these ordinary differential equations is presented using state space techniques.

An expression for the state transition matrix of the ordinary differential equations representing the diffusion equation is obtained as a function of n (the order of the approxkation).

Applicutions of the developed theory include a comparison of the minimum energy controls

for the diffusion equation obtained by spatial discretization and obtained by harmonic truncation.

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