Definition
It is Numerical Method used to find the approximate solution of an 221106 Ordinary Differential Equations an explicit predictor-corrector method that combines Euler’s method (Predictor) with the trapezoidal rule (Corrector) to achieve higher accuracy.
Formula
Derivation
Starting point: The exact solution satisfies
Step 1: Apply trapezoid rule to approximate the integral:
where .
Step 2: Replace exact values with approximations:
- (known)
- (unknown)
This gives:
Step 3: Make explicit by approximating on the right side using Euler’s method:
Step 4: Final Euler-Heun formula:
Properties of Euler-Heun:
- Explicit method (no implicit equation to solve)
- One-step method (uses only to compute )
- Consistency order 2 (local error , global error )
- 2 stages: requires 2 evaluations of per step
- Runge-Kutta method of order 2
- Stability region larger than Euler’s method
- Also called improved Euler or modified Euler method