Abstract
In this paper, an efficient method based on Quasi-Newton's method and the simpliffied reproducing kernel method is proposed for solving nonlinear singular boundary value problems. For the Quasi-Newton's method the convergence order is studied. The uniform convergence of the numerical solution as well as its derivatives are also proved. Numerical examples are given to demonstrate the efficiency and stability of the proposed method. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.
Highlights
By combining with Newton iteration and modifying the reproducing kernel method, we will find the numerical solutions of equation (1.1)
In this paper, we propose a new approach for solving nonlinear singular boundary value problem
The approximate solution can be obtained after iterative computation
Summary
We consider the following nonlinear singular boundary value problem with Neumann and Robin boundary conditions: u (x) +. The authors [1] use B-spline functions to develop a numerical method for computing approximation to the solution of equation (1.1). Numerical solution of equation (1.1) based on improved differential transform method(IDTM) has been proposed by the authors in [10]. The similar method based on IDTM works well for the other type of nonlinear boundary value problems [11]. These numerical methods are efficient and have many advantages, a lot of computational work or a high degree of smoothness are needed. By combining with Newton iteration and modifying the reproducing kernel method, we will find the numerical solutions of equation (1.1). Our method can reduce computation cost and provide highly accurate global approximate solutions
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