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

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 functions to obtain analytic solutions in a uniform form rapidly convergent series the posed Sobolev space. Using Gram-Schmidt orthogonality process, complete orthogonal essential are obtained compact field encompass Fourier expansion with help of properties reproduction. Consequently, by applying standard RKHS method each subinterval, approximate that converge uniformly exact obtained. For purpose, several numerical examples tested show proposed algorithm’s superiority, simplicity, and efficiency. gained results indicate suitable linear nonlinear stiffness systems over extensive duration giving highly accurate outcomes.