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CLC number: O241.81
On-line Access: 2024-08-27
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SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS
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SHAO Jian, Li Da-kan. SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS[J]. Journal of Zhejiang University Science A, 2000, 1(3): 331-336.
@article{title="SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS",
author="SHAO Jian, Li Da-kan",
journal="Journal of Zhejiang University Science A",
volume="1",
number="3",
pages="331-336",
year="2000",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2000.0331"
}
%0 Journal Article
%T SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS
%A SHAO Jian
%A Li Da-kan
%J Journal of Zhejiang University SCIENCE A
%V 1
%N 3
%P 331-336
%@ 1869-1951
%D 2000
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2000.0331
TY - JOUR
T1 - SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS
A1 - SHAO Jian
A1 - Li Da-kan
J0 - Journal of Zhejiang University Science A
VL - 1
IS - 3
SP - 331
EP - 336
%@ 1869-1951
Y1 - 2000
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2000.0331
Abstract: A proposed method for finding an approximate solution of the nonlinear ordinary differential equations two-point boundary value problem is proposed. It simplifies the problem approximately to a problem of solving a set of nonlinear algebraic equations. The basic idea of the method is to utilize the properties of orthogonal polynomials and the approximate operational matrices of the nonlinear functional f(x(t),u(t),t), and also the transformation matrix between the back vector and the current time vector for the general orthogonal polynomials. A method for solving the nonlinear two-point boundary value problems for descriptor systems is also given.
[1]Chang, Y.F., and Lee, T.T., 1986. Application of general orthogonal polynomials to the optimal control of linear systems. Int. J. Control, 43(4):1283-1304.
[2]Cang, R.Y., and Yang, S,Y.,1986. Solution of linear two-point boundary value problems by generalized orthogonal polynomials and application. Int. J. Control, 43(6):1785-1802.
[3]Horng, I.R., and Chou, J. H., 1987. Solution of linear two-point boundaryvalue problems via shifted Chebyshev series. Int. J. Systems Sci., 18(2):293-300.
[4]Luke, Y.,1969. The special Functions and their Approximations, Vols I and II, Academic Press, New York.
[5]Razzaghi, M., 1987. Current Trends in Matrix Theory, Elsevier, New York. p.267-271.
[6]Razzaghi, M.,and Razzaghi, M. A., 1989. Solution of linear two-point boundary value problems via Taylor series. Int. J. Systems Sci., 20(11):2075-2084.
[7]Szego, G., 1975. Orthogonal Polynomials, 4th edition American Mathematical Society, New York.
[8]Tsay,S.C., and Lee, T.T., 1987. Analysis and optimal control of linear time-varying via general orthogonal polynomials. Int.J.System Sci., 18(8):1579-1594.
[9]Wang, J.Q., and Wang, S.Y., 1992. Approximation of nonlinear functionals via general orthogonal polynomials. Int.J.Systems Sci., 23(8):1261-1276.
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