Numerical Methods Solver for Differential Equations

Description

This app solves ordinary differential equations written in the form:

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

How to enter the problem

• Enter the order of the differential equation.
• Enter the right-hand side only.
• Use:
  • y0 for y
  • y1 for y'
  • y2 for y''
  • and so on
• Enter initial conditions as comma-separated values at x = x0.

For an equation of order n, enter exactly n initial conditions:

• y(x0), y'(x0), y''(x0), ..., y^(n-1)(x0)

Examples

First-order

• Equation: y' = y + 2x - x^2
• Order: 1
• RHS: y0 + 2*x - x**2
• Initial conditions: 1

Second-order

• Equation: y'' = -y
• Order: 2
• RHS: -y0
• Initial conditions: 0,1

Third-order

• Equation: y^(3) = x + y2 - 2*y1 + y0
• Order: 3
• RHS: x + y2 - 2*y1 + y0
• Initial conditions: 1,0,-1

Methods available

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

Developed by Jude Okolie