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    Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

    Radwan Abu-Gdairi1, Shatha Hasan2, Shrideh Al-Omari3,*, Mohammad Al-Smadi2,4, Shaher Momani4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 299-313, 2022, DOI:10.32604/cmes.2022.017010

    Abstract In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose,… More >

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