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Numerical solution of delay systems containing inverse time by hybrid functions. (English) Zbl 1090.65089
Summary: The hybrid functions consisting of general block-pulse functions and Legendre polynomials are presented to solve delay systems containing inverse time. The direct algorithm for a product of a matrix function and a vector function is given. The general operational matrix is introduced. The delay function and inverse time function are expanded by hybrid functions. The approximate solution of delay systems containing inverse time is derived. Numerical examples illustrate that the algorithms are applicable.

MSC:
65L05Initial value problems for ODE (numerical methods)
34K28Numerical approximation of solutions of functional-differential equations
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References:
[1] Marzban, H. R.; Razzaghi, M.: Solution of time-varying delay systems by hybrid functions. Math. comput. Simul. 64, 597-607 (2004) · Zbl 1039.65053
[2] Sannuti, P.: Analysis and synthesis of dynamic systems via block-pulse functions. Proc. inst. Elect. eng. 124, 569-571 (1977)
[3] Rao, G. P.; Sivakumar, L.: Analysis and synthesis of dynamic systems containing time-delays via block-pulse functions. Proc. IEE 125, 1064-1068 (1978)
[4] Chen, W. L.; Shih, Y. P.: Shift Walsh matrix and delay differential equations. IEEE trans. Autom. control 23, 265-280 (1978) · Zbl 0388.93029
[5] Razzaghi, M.; Razzaghi, M.: Fourier series approach for the solution of linear two-point boundary value problems with time-varying coefficients. Int. J. Syst. sci. 21, 1783-1794 (1990) · Zbl 0712.34015
[6] Lee, H.; Kung, F. C.: Shifted Legendre series solution and parameter estimation of linear delayed systems. Int. J. Syst. sci. 16, 1249-1256 (1985) · Zbl 0568.93028
[7] Horng, I. R.; Chou, J. H.: Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series. Int. J. Control 41, 1221-1234 (1985) · Zbl 0562.93034
[8] Kung, F. C.; Lee, H.: Solution and parameter estimation of linear time-invariant delay systems using Laguerre polynomial expansion. Trans. ASME J. Dyn. syst. Measur. control 105, 297-301 (1983) · Zbl 0525.93036
[9] Maleknejad, K.; Mahmoudi, Y.: Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions. Appl. math. Comput. 149, 799-806 (2004) · Zbl 1038.65147
[10] Razzaghi, M.; Marzban, H. R.: Direct method for variational problems via hybrid of block-pulse and Chebyshev functions. Math. probl. Eng. 6, 85-97 (2000) · Zbl 0987.65055
[11] Razzaghi, M.; Marzban, H. R.: A hybrid analysis direct method in the calculus of variations. Int. J. Comput. math. 75, 259-269 (2000) · Zbl 0969.49014