ODE Solver Lab

Developed by Gauransh Bansal · LinkedIn

dy/dx = f(x, y)

Initial x0

Initial y0

Step Size (h)

Max Steps

Enabled Solvers Click (i) for guide

Euler Method (Red)

Heun / Imp. Euler (Yellow)

Runge-Kutta 4 / RK4 (Cyan)

Step Details Method

Step Calculations

RK4 solver

Solver Guide

Euler's Method 1st Order

Euler's method is the simplest numerical integration technique. It computes the derivative (slope) at the current point and moves along that tangent line directly for step interval \( h \):

Heun / Improved Euler 2nd Order

Heun's method improves on Euler by predicting the next coordinate first (predictor step \( k_1 \)), calculating the slope at that predicted point (\( k_2 \)), and using the average of both slopes:

Runge-Kutta 4 (RK4) 4th Order

The RK4 method samples four slopes within the interval: \( k_1 \) at the start, \( k_2 \) and \( k_3 \) at the midpoints, and \( k_4 \) at the end. It takes a weighted average of these samples: