Ordinary Differential Equations (ODEs) using power series expansion methods such as Taylor’s series.
Detailed Experiment Steps:
- Theoretical Preparation
- Study ODE power series method
- Understand mathematical principles
- Review Taylor series expansion
- System Setup
- Launch web-based ODE solver
- Verify computational tools
- Check mathematical libraries
- Equation Selection
- Choose differential equation
- Ensure proper mathematical format
- Select equation complexity
- Initial Condition Configuration
- Set initial x value (x0)
- Define initial y value (y0)
- Determine computational range
- Simulation Parameters
- Input differential equation
- Specify series expansion terms
- Set x-axis range
- Configure initial conditions
- Numerical Simulation
- Click "Simulate" button
- Generate power series coefficients
- Analyze solution trajectory
- Observe graphical representation
- Result Analysis
- Examine series coefficients
- Interpret mathematical representation
- Assess solution accuracy
- Compare different equation behaviors