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Journal of Vibration and Control
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Numerical Solution of Linear Time-Varying Differential Equations using the Hybrid of Block-pulse and Rationalized Haar Functions

B. Arabzadeh

Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran

M. Razzaghi

Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA and Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran, razzaghi{at}math.msstate.edu

Y. Ordokhani

Department of Mathematics, Alzahra University, Tehran, Iran

A numerical method for finding the solution of linear time-varying differential equations is proposed. The properties of the hybrid functions, which consist of block-pulse functions plus rationalized Haar functions, are presented. The properties of the hybrid functions together with the operational matrices of integration and product are then utilized to reduce the solution of differential equations to the solution of algebraic equations. Examples are included to demonstrate the validity and applicability of the technique.

Key Words: Hybrid • rationalized Haar functions • block-pulse functions • differential equations

Journal of Vibration and Control, Vol. 12, No. 10, 1081-1092 (2006)
DOI: 10.1177/1077546306069121
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