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math.NA2021★ 2 cited
Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases
Xiaolong Zhang, John P. Boyd
When solving differential equations by a spectral method, it is often convenient to shift from Chebyshev polynomials with coefficients to modified basis function…
math.NA2017★ 15 cited
High order analysis of the limit cycle of the van der Pol oscillator
Paolo Amore, John P. Boyd, Francisco M. Fernández
We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the…
math.NA2010
A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon
John P. Boyd
When a function is singular at a point on the real axis, its Fourier series, when truncated at the -th term, gives a pointwise error of only over the ent…