Solutions of convolution integral and integral equations via double general orthogonal polynomialsTSU-TIAN LEEt and YIH-FONG CHANGZ Double general orthogonal polynomials are developed in this work to approximate the solutions of convolution integrals, Volterra integral equations, and Fredholm integral equations. The proposed method reduces the computations of integral equations to the successive solution of a set of linear algebraic equations in matrix form; thus, the computational complexity is considerably simplified. Furthermore, the solutions obtained by the general orthogonal polynomials include as special cases solutions by Chebyshev polynomials, Legend re polynomials, Laguerre polynomials, or Jacobi polynomials. A comparison of the results obtained via several diflerent classical orthogonal polynomial approximations is also presented.
Analysis and identification of linear distributed systems via double general orthogonal polynomials TSU-TIAN LEEt and YIH-FONG CHANGt Double general orthogonal polynomials are used for the analysis and parameter estimation of linear distributed systems. The formulating of algorithms for analysing and for estimating the parameters of linear distributed systems is straightforward and convenient for digital computation. Illustrative examples are given to demonstrate the availability of the proposed method.
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