Theoretical Foundation

Power Series Method is a sophisticated numerical technique for solving Ordinary Differential Equations (ODEs) by expanding the solution as an infinite series around a specific point. Mathematical Principles

Solution representation: y(x) = Σ(aₙ(x-x₀)ⁿ) Derives solution coefficients through recursive derivation Approximates complex nonlinear differential equations

Numerical Approximation Techniques

Taylor Series Expansion

Generates solution by successive differentiation Converts differential equation into algebraic series Provides analytical approximation

Coefficient Calculation

Iterative derivation of function Systematic coefficient generation Handles complex nonlinear equations

Experimental Objectives

Demonstrate power series solution methodology Compare numerical approximation for different ODEs Visualize solution trajectories