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• W2031205500 abstract "We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving boundary value problems (BVPs), integral and integro-differential equations. The proposed approach recasts the original problems into their integral formulations, which are then discretized into linear systems of algebraic equations using Gegenbauer integration matrices (GIMs). The resulting linear systems are well-conditioned and can be easily solved using standard linear system solvers. A study on the error bounds of the proposed method is presented, and the spectral convergence is proven for two-point BVPs (TPBVPs). Comparisons with other competitive methods in the recent literature are included. The proposed method results in an efficient algorithm, and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems. The proposed method can be applied on a broad range of mathematical problems while producing highly accurate results. The developed numerical scheme provides a viable alternative to other solution methods when high-order approximations are required using only a relatively small number of solution nodes." @default.
• W2031205500 created "2016-06-24" @default.
• W2031205500 creator A5056556906 @default.
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• W2031205500 date "2013-01-01" @default.
• W2031205500 modified "2023-10-16" @default.
• W2031205500 title "Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices" @default.
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• W2031205500 doi "https://doi.org/10.1016/j.cam.2012.05.024" @default.
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