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### Operational Matrix Basic Spline Wavelets of Derivative for linear Optimal Control Problem

Maha Delphi, Suha SHIHAB

#### Abstract

The main importance goal in this paper is studying the interesting properties of basic spline wavelets functions (BSWFs) and derived some new basic formulations of them. The important operational matrix is devoted in two ways, the first one is the derivative of BSWFs in terms of the lower order of  BSWFs  while the second is the derivative of BSWFs in terms of the same order of BSWFs.  The expression formula for the operational matrix  is determined for different orders. In addition an useful formulas concerning the power function and BSMSFs are also presented. The polynomials and wavelets expansions together with operational matrices can be employed to solve problems in applied science and other fields of approximation theory. In this work, two optimal control problem are tested with the aid of operational matrix of derivative for BSWFs with satisfactory results.

#### Keywords

Basic spline wavelets; Operational matrix; Linear optimal control problem

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DOI: http://dx.doi.org/10.18686/esta.v6i2.91

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