Examples for

Numerical Differential Equation Solving

Many numerical methods exist for solving ordinary and partial differential equations. Through Wolfram|Alpha, access a wide variety of techniques, such as Euler's method, the midpoint method and the Runge–Kutta methods. Compare different methods, examine the effect of step size changes and get the symbolic details of the calculation.

Use numerical methods to solve ordinary differential equations.

Solve an ODE using a specified numerical method:

Runge-Kutta method, dy/dx = -2xy, y(0) = 2, from 1 to 3, h = .25

use Euler method y' = -2 x y, y(1) = 2, from 1 to 5

solve {y'(x) = -2 y+x, y(1) = 2} with midpoint method

solve y'(x) = -2 y+x apply heun method

{y'(x) = -2 y, y(0)=1} from 0 to 2 by backward Euler

{y'(x) = -2 y, y(0)=1} from 0 to 2 by implicit midpoint

Specify an adaptive method:

solve {y'(x) = -2 y, y(0)=1} from 0 to 10 using r k f algorithm

{y'(x) = -2 y, y(0)=1} from 0 to 10 by Bogacki-Shampine method

Compare the performance of different methods:

forward euler method vs. backward euler for y'=-x y, y(0)=1

More examples