Abstract
Linear barycentric rational method for solving two-point boundary value equations is presented. The matrix form of the collocation method is also obtained. With the help of the convergence rate of the interpolation, the convergence rate of linear barycentric rational collocation method for solving two-point boundary value problems is proved. Several numerical examples are provided to validate the theoretical analysis.
Highlights
By using the notation of the differential matrix, equation (13) is denoted as matrices in the form of n
We know that the central difference method can achieve quadratic convergence and the convergence order is the same as that of d 3
We consider the variable coefficient of two-point boundary value equations with the boundary
Summary
With the error function of difference formula e(x) ≔ u(x) − r(x) x − xi · · · x − xi+dxi, xi+1, . . . , xi+d, xf,. E following Lemma has been proved by Jean-Paul. Let u(x) be the solution of (1) and un(x) is the numerical solution, we have. Based on the above lemma, we derive the following theorem. Let un(x): Tun(x) f(x), u∗n (x): Tu∗n (x) f∗(x), and f(x) ∈ C[a, b], we have. un(x) − u∗n (x) ≤ Chd− 1. un(x) − u∗n (x) ≤ j n0 Mj(x)|Te(x)| ≤ Chd− 1. We know that the central difference method can achieve quadratic convergence and the convergence order is the same as that of d 3. When d >3, the convergence of the barycentric rational method is better than that of the central difference method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
