amyammerman/Numerical_Method_Solver

1---2title: Numerical Methods Solver3emoji: 📘4colorFrom: blue5colorTo: green6sdk: gradio7app_file: app.py8pinned: false9---10 11# Numerical Methods Solver for Differential Equations12 13This app solves ordinary differential equations of the form:14 15y^(n) = f(x, y, y', y'', ..., y^(n-1))16 17using the following numerical methods:18 19- Forward Euler20- Backward Euler21- Modified Euler (Heun)22- Runge-Kutta 4th Order (RK4)23 24## Input format25 26Enter:27 28- the order of the ODE29- the right-hand side30- the initial conditions31- x032- x_end33- the step size34- one or more numerical methods35- optional exact solution for comparison36 37## Variable notation38 39In the right-hand side, use:40 41- y0 for y42- y1 for y'43- y2 for y''44- etc.45 46## Examples47 48### First-order ODE49y' = y + 2x - x^2, y(0) = 150 51Use:52- Order: 153- RHS: y0 + 2*x - x**254- Initial conditions: 155 56### Second-order ODE57y'' = -y, y(0) = 0, y'(0) = 158 59Use:60- Order: 261- RHS: -y062- Initial conditions: 0,163 64### Third-order ODE65y^(3) = x + y2 - 2*y1 + y066 67Use:68- Order: 369- RHS: x + y2 - 2*y1 + y070- Initial conditions: 1,0,-171 72## Notes73 74This app is designed for initial value problems and converts higher-order ODEs into first-order systems internally.75 76Developed by Amy Ammerman77