In recent decades, barycentric interpolation methods have attracted increasing attention in the field of numerical methods because of stability and have become a powerful tool for investigating boundary value problems, initial problems, nonlinear problems, and so on. There are barycentric Lagrange interpolation methods and barycentric rational interpolation methods which are different from the weight function.

The analysis of barycentric interpolation methods still faces many new challenges. When employing barycentric interpolation methods to solve practical problems, it is crucial to be able to completely characterize the properties of the barycentric interpolation methods, especially for higher dimensional problems.

This Special Issue aims to gather research focusing on the development of barycentric interpolation methods and their applications. We invite authors to submit original research as well as review articles that reveal the properties of barycentric interpolation methods and their applications for solving practical problems.

Potential topics include but are not limited to the following:

• Boundedness analysis, stability
• Asymptotical analysis
• Barycentric interpolation methods for integral equations
• Barycentric interpolation methods for differential equations
• Barycentric interpolation methods for interface problems
• Numerical computation analysis
• Stability of barycentric rational interpolation methods