Cubic Spline Interpolation with Fixed Boundary Conditions

This MATLAB program demonstrates cubic spline interpolation under fixed boundary conditions, providing practical implementation insights for this numerical analysis technique. Cubic spline interpolation is a powerful data fitting method that constructs piecewise cubic polynomials to smoothly approximate discrete datasets, enabling effective data smoothing and prediction capabilities. The program accepts user-provided datasets and automatically generates a complete cubic spline interpolation function. Key algorithmic components include: setting fixed boundary conditions for first/second derivatives, solving the tridiagonal system of linear equations for spline coefficients, and constructing piecewise polynomial segments. The implementation handles boundary value specification through dedicated input parameters and utilizes MATLAB's built-in matrix operations for efficient computation. Visualization features include automatic generation of interpolation curves, allowing users to analyze the smoothness and accuracy of the fitted data. The code employs MATLAB's plotting functions to display both original data points and the interpolated curve, facilitating comparative analysis. For researchers and engineers working with numerical methods, this program offers valuable hands-on experience in implementing spline interpolation algorithms while demonstrating practical applications in data approximation and curve fitting scenarios. The implementation highlights important MATLAB functions such as matrix solvers for linear systems and polynomial evaluation techniques, making it an excellent educational resource for understanding both the mathematical foundations and programming aspects of spline interpolation methods.