Numerical Approximations Using Chebyshev Polynomial Expansions

Details Numerical Approximations Using Chebyshev Polynomial Expansions Numerical Approximations Using Chebyshev Polynomial Expansions

1999-01-07

arxiv.org/abs/physics/9901005v3

J. Phys. A: Math. Gen. 35, 731 (2002)

Physics

Computational Physics

minor wording changes, some typos have been eliminated

Scientific paper

10.1088/0305-4470/35/3/317

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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