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| ASCII Text | x | ||
| J.R. Rowland, W.M. Holmes, "A Variational Approach to Digital Integration," IEEE Transactions on Computers, vol. 20, no. 8, pp. 894-900, August, 1971. | |||
| BibTex | x | ||
| @article{ 10.1109/T-C.1971.223367, author = {J.R. Rowland and W.M. Holmes}, title = {A Variational Approach to Digital Integration}, journal ={IEEE Transactions on Computers}, volume = {20}, number = {8}, issn = {0018-9340}, year = {1971}, pages = {894-900}, doi = {http://doi.ieeecomputersociety.org/10.1109/T-C.1971.223367}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Variational Approach to Digital Integration IS - 8 SN - 0018-9340 SP894 EP900 EPD - 894-900 A1 - J.R. Rowland, A1 - W.M. Holmes, PY - 1971 KW - Computational accuracy versus speed KW - digital integration KW - hybrid simulation KW - nonlinear ordinary differential equations KW - numerical approximations KW - real-time digital simulation KW - state transition method KW - variational technique. VL - 20 JA - IEEE Transactions on Computers ER - | |||
Variational equations are derived as a preliminary step in determining efficient digital integration techniques for nonlinear dynamical systems. The variational approach is applied initially to linear time-invariant systems to introduce the basic concept and then to nonlinear time-varying systems. For systems containing both linear and nonlinear parts, a combination technique which uses the exact difference equation for the linear part is developed. Higher order variational equations are also derived and compared on a simple system. Numerical approximations for solving these variational equations are discussed and illustrated for a second-order mildly nonlinear example. A significant improvement in both accuracy and execution time is realized over results obtained by the conventional fourth-order Runge?Kutta method. Finally, the new approach is discussed from the viewpoint of computational experience and special limitations for practical applications.
Index Terms:
Computational accuracy versus speed, digital integration, hybrid simulation, nonlinear ordinary differential equations, numerical approximations, real-time digital simulation, state transition method, variational technique.
Citation:
J.R. Rowland, W.M. Holmes, "A Variational Approach to Digital Integration," IEEE Transactions on Computers, vol. 20, no. 8, pp. 894-900, Aug. 1971, doi:10.1109/T-C.1971.223367
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