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Journal of Zhejiang University SCIENCE A 2000 Vol.1 No.3 P.331-336

http://doi.org/10.1631/jzus.2000.0331


SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS


Author(s):  SHAO Jian, Li Da-kan

Affiliation(s):  Dept.of Mathematics, Zhejiang University, Hangzhou, 310027, China.

Corresponding email(s): 

Key Words:  nonlinear systems, two-point boundary value problems, approximate solution, 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.

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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.

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Reference

[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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