Runge-Kutta Runge-Kutta (RK4) Method Calculator Numerically solve a first-order ODE \( \frac{dy}{dx} = f(x, y) \) using the classical Runge–Kutta method of order 4 (RK4). We show every intermediate slope (k1–k4) and the resulting y values. 1. Problem setup Use JavaScript/Math syntax: x + y , x*y , Math.sin(x) , y - x*x . We already expose common Math functions via with(Math){...} . dy/dx = f(x, y) Number of steps x₀ y(x₀) Step size h Run RK4 2. Solution steps No computation yet. Fill the form and click “Run RK4”. Runge–Kutta 4th order formula Given \(\frac{dy}{dx} = f(x, y)\) and a current point \((x_n, y_n)\) with step \(h\): k₁ = f(xₙ, yₙ) k₂ = f(xₙ + h/2, yₙ + h·k₁/2) k₃ = f(xₙ + h/2, yₙ + h·k₂/2) k₄ = f(xₙ + h, yₙ + h·k₃) yₙ₊₁ = yₙ + (h/6)(k₁ + 2k₂ + 2k₃ + k₄) This method is popular because it strikes an excellent balance between accuracy and computational cost. Tips If the solution diverges, try a smaller step size \(h\). For stiff ODEs, RK4 might not be the best choice. Always check your function syntax if you get NaN results. Related Math Tools Core Math & Algebra Graphing & Visualization Correlation Coefficient Confidence Interval When RK4 is overkill If you just need a quick rough value, Euler’s method is simpler. RK4 is ideal when you want good accuracy but don’t want to implement adaptive step-size methods.

Calculators in Runge-Kutta Runge-Kutta (RK4) Method Calculator Numerically solve a first-order ODE \( \frac{dy}{dx} = f(x, y) \) using the classical Runge–Kutta method of order 4 (RK4). We show every intermediate slope (k1–k4) and the resulting y values. 1. Problem setup Use JavaScript/Math syntax: x + y , x*y , Math.sin(x) , y - x*x . We already expose common Math functions via with(Math){...} . dy/dx = f(x, y) Number of steps x₀ y(x₀) Step size h Run RK4 2. Solution steps No computation yet. Fill the form and click “Run RK4”. Runge–Kutta 4th order formula Given \(\frac{dy}{dx} = f(x, y)\) and a current point \((x_n, y_n)\) with step \(h\): k₁ = f(xₙ, yₙ) k₂ = f(xₙ + h/2, yₙ + h·k₁/2) k₃ = f(xₙ + h/2, yₙ + h·k₂/2) k₄ = f(xₙ + h, yₙ + h·k₃) yₙ₊₁ = yₙ + (h/6)(k₁ + 2k₂ + 2k₃ + k₄) This method is popular because it strikes an excellent balance between accuracy and computational cost. Tips If the solution diverges, try a smaller step size \(h\). For stiff ODEs, RK4 might not be the best choice. Always check your function syntax if you get NaN results. Related Math Tools Core Math & Algebra Graphing & Visualization Correlation Coefficient Confidence Interval When RK4 is overkill If you just need a quick rough value, Euler’s method is simpler. RK4 is ideal when you want good accuracy but don’t want to implement adaptive step-size methods..