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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Kawarai, S. |
| Copyright Year | 2004 |
| Description | Author affiliation: Res. Lab., Anritsu Corp., Atsugi, Japan (Kawarai, S.) |
| Abstract | Differential equations are frequently used to analyze and design analog circuits and numerically solved from computation of difference equations. The equivalent difference equations are obtained by using the solutions or the Laplace transform of the corresponding differential equations for exact discretization. Here, we propose a direct method for exact discretization obtaining the equivalent difference equation whose solution is equal to the solution of a differential equation at any discrete periodic point. The direct method greatly differs from the existing method in needing neither the solutions nor the Laplace transform of differential equations. The equivalent difference equations are readily produced by direct transform of replacing (d/dt-/spl alpha/)x(t) with (1-e/sup /spl alpha/T/E/sup -1/)x/sub n/ in factorized differential equations (where x/sub n/ equal to by definition x(nT), /spl alpha/ is a constant, T the sampling period, and E the shift operator defined by E/sup -1/x/sub n/=x/sub n-1/). The method is applied to some examples including ordinary differential equations (ODEs) and nonlinear one of logistic equation which represents the chaos behavior. The proposed method is the simplest, easiest and fastest method ever, and very important and useful for generating exact numerical solutions of ODEs. |
| File Size | 306315 |
| File Format | |
| ISBN | 078038346X |
| DOI | 10.1109/MWSCAS.2004.1353904 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2004-07-25 |
| Publisher Place | Japan |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Differential equations Difference equations Laplace equations Analog circuits Analog computers Circuit analysis computing Discrete transforms Sampling methods Logistics Nonlinear equations |
| Content Type | Text |
| Resource Type | Article |
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