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Numerical Approximations Using Chebyshev Polynomial Expansions

Bogdan Mihaila·Ioana Mihaila
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Abstract

We 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 connection to 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.

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Bogdan Mihaila, Ioana Mihaila. 2001-10-31. Numerical Approximations Using Chebyshev Polynomial Expansions. https://doi.org/10.1088/0305-4470%2F35%2F3%2F317

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