Numerical Methods2D

Ordinary Differential Equations - Theory & Concepts - Euler Method

Numerical solutions for initial-value and boundary-value problems of ordinary differential equations.

Solving the initial value problem $\frac{dy}{dx} = -2x^3 + 12x^2 - 20x + 8.5$ , with $y(0) = 1$ .

Step Size (h): 0.50

0.1 (More Accurate)2.0 (Less Accurate)

True y(4)

3.0000

Euler Approx y(4)

7.0000

True Percent Relative Error:

133.33%

Euler's Formula

y_{i+1} = y_i + f(x_i, y_i)h

Euler's method truncates the Taylor series after the first derivative. Decreasing the step size

h

reduces this truncation error and improves accuracy.

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