Numerical methods for ordinary differential equations

Summary

Numerical methods for ordinary differential equations compute approximate values of the solution of an initial value problem $y' = f(t, y)$, $y(t_0) = y_0$, at a finite set of times. Most ordinary differential equations have no solution in closed form, so these methods are the main way to solve them in science and engineering. The two big families are one-step methods, such as the Euler method and the Runge–Kutta methods, and linear multistep methods. Their theory studies consistency, measured by the local truncation error, together with stability and convergence. It pays special attention to stiff equations and to adaptive step size control.