TY - EJOU AU - Abu-Gdairi, Radwan AU - Hasan, Shatha AU - Al-Omari, Shrideh AU - Al-Smadi, Mohammad AU - Momani, Shaher TI - Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis T2 - Computer Modeling in Engineering \& Sciences PY - 2022 VL - 130 IS - 1 SN - 1526-1506 AB - 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, several numerical examples are tested to show proposed algorithm’s superiority, simplicity, and efficiency. The gained results indicate that the multi-step RKHS method is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes. KW - Multi-step approach; reproducing kernel Hilbert space method; stiffness system; error analysis; numerical solution DO - 10.32604/cmes.2022.017010