Abstract
This paper is devoted to the numerical treatment of a class of higher-order multi-point boundary value problem-s(BVPs). The method is proposed based on the Lagrange interpolation collocation method, but it avoids thenumerical instability of Lagrange interpolation. Numerical results obtained by present method compare with othermethods show that the present method is simple and accurate for higher-order multi-point BVPs, and it is eectivefor solving six order or higher order multi-point BVPs.
Highlights
Collocation method as a numerical calculation method for solving differential equations, it has many merits, such as calculation formula is simple, program implementation is convenient
Chebyshev point as interpolation nodes, use barycentric interpolation collocation method establish the dierential matrix of function to solve multi-point boundary value problems(BVPs)
In this paper, we devote to the numerical treatment of a class of higher-order multi-point solving higher-order multi-point BVPs
Summary
Collocation method as a numerical calculation method for solving differential equations, it has many merits, such as calculation formula is simple, program implementation is convenient. Use Lagrange interpolation collocation method to solve differential equations, when select too many nodes, Lagrange collocation formula will be not numerical instability, the famous Runge phenomenon illustrates the problem[1]. Barycentric interpolation collocation method has excellent numerical instability[2]. Chebyshev point as interpolation nodes, use barycentric interpolation collocation method establish the dierential matrix of function to solve multi-point boundary value problems(BVPs). In [4],[5], Lin and Wu use the reproducing kernel to solve the following boundary value problems(BVPs). We use barycentric interpolation to solve (1) , several numerical examples are given to demonstrate the efficiency of the present method. The present method compared with the others methods, reveals that the present method is more effective and convenient
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