An Enhanced Chebyshev Collocation Method Based on the Integration of Chebysehv Interpolation
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In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme ofthe generalized Chebyshev interpolations for solving stiff initial value problems. Unlike the formererror embedded Chebyshev collocation method (CCM), the enhanced scheme calculatesthe 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 algorithmturns 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 numericallymore efficient compared to existing methods.
Abstract
In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme ofthe generalized Chebyshev interpolations for solving stiff initial value problems. Unlike the formererror embedded Chebyshev collocation method (CCM), the enhanced scheme calculatesthe 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 algorithmturns 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 numericallymore efficient compared to existing methods.
참고문헌 (21)
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