amyammerman/Numerical_Method_Solver

Numerical Methods Solver for Differential Equations

This app solves ordinary differential equations of the form:

y^(n) = f(x, y, y', y'', ..., y^(n-1))

using the following numerical methods:

• —Forward Euler
• —Backward Euler
• —Modified Euler (Heun)
• —Runge-Kutta 4th Order (RK4)

Input format

Enter:

• —the order of the ODE
• —the right-hand side
• —the initial conditions
• —x0
• —x_end
• —the step size
• —one or more numerical methods
• —optional exact solution for comparison

Variable notation

In the right-hand side, use:

• —y0 for y
• —y1 for y'
• —y2 for y''
• —etc.

Examples

First-order ODE

y' = y + 2x - x^2, y(0) = 1

Use:

• —Order: 1
• —RHS: y0 + 2x - x*2
• —Initial conditions: 1

Second-order ODE

y'' = -y, y(0) = 0, y'(0) = 1

Use:

• —Order: 2
• —RHS: -y0
• —Initial conditions: 0,1

Third-order ODE

y^(3) = x + y2 - 2*y1 + y0

Use:

• —Order: 3
• —RHS: x + y2 - 2*y1 + y0
• —Initial conditions: 1,0,-1

Notes

This app is designed for initial value problems and converts higher-order ODEs into first-order systems internally.

Developed by Amy Ammerman