Nonlinear Multi-Point Problems Via Chelyshkov Approach

This study addresses a numerical method based on Chelyshkov polynomials for solving nonlinear multi-point boundary value problems (NBVPs). These polynomials are orthogonal on providing a solid basis for approximating solutions. The method converts the nonlinear equations with boundary conditions into a matrix structure and allows solutions to be computed in an efficient manner. The chosen examples demonstrate the method’s accuracy and practical advantages over existing techniques. Beyond NBVPs, the approach can also be applied to a broader class of functional differential equations in fields such as physics, biology, and engineering, offering a robust and adaptable tool for researchers tackling complex problems.