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RESEARCH & SIMULATION LAB

Differential equation solver for numerical models.

Model first-order ordinary differential equations and two-state systems with Euler, Improved Euler, and RK4. Inspect solution curves, phase plots, and numerical tables directly in your browser.

NUMERICAL OUTPUT

Ready to simulate

Runge–Kutta 4 (RK4)
dy/dx

Set the equation, initial values, interval, and method. Your graph, final values, and table will appear here.

Choose a preset or enter an equation, then run a numerical simulation.

MODEL SETUP

Build the numerical experiment

Examples

METHOD NOTE

Euler is fast but less accurate. Heun improves the slope estimate. RK4 is a strong general-purpose fixed-step method. All outputs are numerical approximations.
01

Choose the model

Enter the right-hand side only, such as -2*y + sin(x). Use x, y, and z with supported functions.

02

Set initial conditions

Specify where the numerical experiment begins, its final x value, and a controlled step size.

03

Inspect the approximation

Compare curves, phase behavior, and tables. Reduce the step size when accuracy needs checking.

ABOUT THIS TOOL

Differential Equations Lab

Model first-order ODEs and two-state systems with controlled initial conditions, step sizes, solution curves, phase plots, and numerical tables.

  • First-order ordinary differential equations
  • Two-state numerical systems and phase plots
  • Euler, Improved Euler, and RK4 comparisons

KEY FUNCTIONS

First-order ODEs: y′ = f(x, y)Two-state systems: y′ and z′Euler, Improved Euler (Heun), and RK4Initial conditions and custom interval controlsSolution graph, phase plot, and numerical tableUp to 10,000 controlled numerical steps

LEARN THE METHOD

Short guides for this workflow

GUIDEEuler method for differential equationsUse a fixed step and local slope to estimate a first-order initial value problem.Read →GUIDERunge-Kutta RK4 methodUnderstand four-slope RK4 updates for numerical ordinary differential equations.Read →

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