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Resolution of first- and second-order linear differential equations with periodic inputs by a computer algebra system. (English) Zbl 1184.68654
Summary: In signal processing, a pulse means a rapid change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. A square wave function may be viewed as a pulse that repeats its occurrence periodically but the return to the baseline value takes some time to happen. When these periodic functions act as inputs in dynamic systems, the standard tool commonly used to solve the associated initial value problem (IVP) is Laplace transform and its inverse. We show how a computer algebra system may also provide the solution of these IVP straight forwardly by adequately introducing the periodic input.

MSC:
68W30 Symbolic computation and algebraic computation
34A30 Linear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations
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References:
[1] R. J. Beerends, H. G. ter Morsche, J. C. van den Berg, and E. M. van de Vrie, Fourier and Laplace Transforms, Cambridge University Press, Cambridge, UK, 2003. · Zbl 1035.42002
[2] J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems, McGraw-Hill, New York, NY, USA, 1993.
[3] DERIVETM. The Mathematical Assistant for Your Personal Computer, Texas Instruments, Stafford, Tex, USA, 2000.
[4] M. Legua, J. A. Moraño, and L. M. Sánchez Ruiz, “Generating periodic functions,” WSEAS Transactions on Systems, vol. 3, no. 1, pp. 37-39, 2004. · Zbl 1097.68679
[5] S. Wolfram, The Mathematica\textregistered Book, Wolfram Media/Cambridge University Press, Cambridge, UK, 4th edition, 1999. · Zbl 0924.65002
[6] MATLAB\textregistered . The Language of Technical Computing, The MathWorks, Natick, Mass, USA, 2002.
[7] M. Legua, J. A. Moraño, and L. M. Sánchez Ruiz, “Sine and cosine series representations,” WSEAS Transactions on Mathematics, vol. 3, no. 3, pp. 543-548, 2004. · Zbl 1205.42003
[8] L. M. Sánchez Ruiz, M. Legua, and J. A. Moraño, Matemáticas con DERIVE, Universidad Politécnica de Valencia, Valencia, Spain, 2001.
[9] C. H. Edwards Jr. and D. E. Penney, Ecuaciones Diferenciales Elementales, Prentice Hall, Upper Saddle River, NJ, USA, 1993.
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