Euler's Method Calculator

Differential Equation dy/dx =

Initial x:

Initial y:

End x:

Number of steps:

Step	x	y	dy/dx

Understanding Euler's Method

What is Euler's Method?

Euler's method is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

Key Equations

y(x + h) ≈ y(x) + h * f(x,y)
h = (xₙ - x₀)/n
yᵢ₊₁ = yᵢ + h * f(xᵢ,yᵢ)
xᵢ₊₁ = xᵢ + h

Advanced Concepts

Error Analysis

Local truncation error: O(h²)

Global truncation error: O(h)

Stability conditions

Error propagation

Method Variations

Forward Euler

Backward Euler

Modified Euler

Predictor-Corrector

Applications

Population dynamics

Chemical kinetics

Circuit analysis

Heat transfer

Limitations

Step size sensitivity

Error accumulation

Stiff equations

Numerical instability

Numerical Analysis

Convergence

Consistency

Stability

Order of accuracy

Error bounds

Implementation

Step size selection

Error estimation

Adaptive methods

System solving

Related Methods

Runge-Kutta

Adams-Bashforth

Implicit methods

Multistep methods

Practical Aspects

Computational cost

Memory requirements

Parallel implementation

Software tools