Abstract
The numerical solution for a kind of third-order boundary value problems is discussed. With the barycentric rational interpolation collocation method, the matrix form of the third-order two-point boundary value problem is obtained, and the convergence and error analysis are obtained. In addition, some numerical examples are reported to confirm the theoretical analysis.
Highlights
Differential equations can give full play to their mathematical advantages in various disciplines
Many engineering and physical problems can be transformed into the initial boundary value problems of differential equations
Barycentric rational interpolation collocation method means using barycentric interpolation polynomials to find the differential matrix of a function at each discrete point; the solution of the differential equation can be obtained by matrix operation. e barycentric rational interpolation has excellent numerical stability and high approximation accuracy, and the barycentric rational interpolation formula has a compact calculation formula of all order derivatives
Summary
Differential equations can give full play to their mathematical advantages in various disciplines. Many engineering and physical problems can be transformed into the initial boundary value problems of differential equations. In these problems, only a few simple cases can be solved analytically, and most engineering problems need to be solved by numerical methods. We consider the numerical solution of the third-order twopoint boundary value problem, u′′′(x) + pu′′(x) + qu′(x) + ru(x) f(x), a < x < b,. Barycentric rational interpolation collocation method means using barycentric interpolation polynomials to find the differential matrix of a function at each discrete point; the solution of the differential equation can be obtained by matrix operation. Journal of Mathematics method is an effective method for solving boundary value problems of differential equations
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