Bogdan Mihaila and Ioana Mihaila 2002 J. Phys. A: Math. Gen. 35 731 doi:10.1088/0305-4470/35/3/317
Numerical approximations using Chebyshev polynomial expansions: El-gendi's method revisited
Bogdan Mihaila1 and Ioana Mihaila2
Show affiliationsWe present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second-order boundary value problems in fluid dynamics are presented.
- PACS
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02.30.Mv Approximations and expansions
02.60.Jh Numerical differentiation and integration
02.60.Nm Integral and integrodifferential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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34A30 Linear equations and systems, general
41A50 Best approximation, Chebyshev systems
41A10 Approximation by polynomials (For approximation by trigonometric polynomials, see 42A10)
45J05 Integro-ordinary differential equations (See also 34K05, 34K30, 47G20)
- Subjects
- Dates
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Issue 3 (25 January 2002)
Received 12 July 2001, in final form 6 November 2001
Published 11 January 2002
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Numerical approximations using Chebyshev polynomial expansions: El-gendi's method revisited
Bogdan Mihaila and Ioana Mihaila 2002 J. Phys. A: Math. Gen. 35 731
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