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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.

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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