Numerical Methods Suite: Euler ODE Solver, Neville Interpolation, and MATLAB Algorithms

This comprehensive MATLAB package contains a rich collection of numerical algorithms designed to solve various mathematical problems efficiently. For differential equations, the Euler method implementation provides a fundamental numerical approach for solving ordinary differential equations using iterative step-wise approximations. The package includes sophisticated interpolation routines featuring Neville's algorithm - which builds interpolating polynomials through recursive table generation - and Newton interpolation that utilizes divided differences for polynomial construction.

For advanced differential equation solutions, the Taylor method implementation leverages series expansions to achieve higher-order accuracy. In linear algebra computations, the improved square root method (enhanced Cholesky decomposition) efficiently handles symmetric positive definite matrices, while the chasing method (Thomas algorithm) provides optimized solutions for tridiagonal systems. These carefully coded implementations not only enhance mathematical problem-solving skills but also significantly boost productivity through reliable, ready-to-use numerical solutions.

Each algorithm is implemented with proper error handling, vectorization where applicable, and includes clear documentation for easy integration into larger projects. The code follows MATLAB best practices with appropriate preallocation, optimized loops, and mathematical validation checks.