Runge–Kutta RK4 Calculator
Use classical RK4 to integrate y′ = f(x,y) from an initial condition. The tool plots the solution, reports step count and endpoint error, and lets you export the numerical trajectory.
Expression syntax: use explicit multiplication such as 2*y. Supported functions include sin, cos, tan, exp, ln, sqrt and abs.
How this tool works
RK4 combines four slope samples: k₁=f(x,y), k₂=f(x+h/2,y+hk₁/2), k₃=f(x+h/2,y+hk₂/2), k₄=f(x+h,y+hk₃), then yₙ₊₁=yₙ+h(k₁+2k₂+2k₃+k₄)/6.
Example
For y′ = −2y with h=0.1, RK4 should closely track exp(−2x) over the interval while using a fixed step size.
Common questions
What order is RK4?
Classical RK4 has fourth-order global accuracy for sufficiently smooth problems, so reducing h typically decreases truncation error rapidly until floating-point or model effects dominate.
Is RK4 good for stiff equations?
Not necessarily. RK4 is explicit and has a finite stability region. Strongly stiff problems can force impractically small time steps.