Abstract
This paper is concerned with a high-order numerical scheme for nonlinear systems of second-order boundary value problems (BVPs). First, by utilizing quasi-Newton’s method (QNM), the nonlinear system can be transformed into linear ones. Based on the standard Lobatto orthogonal polynomials, we introduce a high-order Lobatto reproducing kernel method (LRKM) to solve these linear equations. Numerical experiments are performed to investigate the reliability and efficiency of the presented method.
Highlights
Nonlinear systems of second-order boundary value problems (BVPs) are widely used in applied physics, mechanical engineering, biology, etc
Nonlinear systems of second-order BVPs are widely used in applied physics, mechanical engineering, biology, etc
We mainly focus on numerical solutions for such problems
Summary
Nonlinear systems of second-order BVPs are widely used in applied physics, mechanical engineering, biology, etc. We mainly focus on numerical solutions for such problems. To the best of our knowledge, research studies on numerical methods for nonlinear systems of second-order BVPs were seldom reported. QNM [12] and simplified reproducing kernel method (SRKM) [13] are combined to design a numerical method for solving nonlinear systems (1). It is worth noting that QNM acts directly on operator equations to linearize nonlinear problems by Frechet derivative. Motivated by designing RKM of high-order accuracy, we establish a reproducing kernel space with polynomial form by applying the wellknown Lobatto orthogonal polynomials.
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