• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.287-299
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• 2017

In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme of the generalized Chebyshev interpolations for solving stiff initial value problems. Unlike the former error embedded Chebyshev collocation method (CCM), the enhanced scheme calculates the solution and its truncation error based on the interpolation of the derivative of the true solution and its integration. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the $7^{th}$ convergence order and the A-stability without any loss of advantages for CCM. Throughout a numerical result, we assess the proposed method is numerically more efficient compared to existing methods.