Improved Euler Method Calculator

About this calculator

Heun's method — also called the improved or modified Euler method — is a second-order Runge-Kutta technique for numerically solving ordinary differential equations. It first takes a standard Euler “predictor” step, then averages the slope at the starting point with the slope at the predicted endpoint to compute a more accurate “corrected” value.

That averaging reduces the local truncation error from O(h²) for plain Euler down to O(h³), a meaningful accuracy gain for the same step size. This calculator performs one such step for y' = a·x + b·y and is used in numerical methods coursework and engineering/physics simulations as a stepping stone between simple Euler integration and higher-order solvers like RK4.