Question Bank • QB_EM_120
NAT • 2 Marks
Section 1: Engineering Mathematics
Numerical Methods
Subtopic: Numerical solutions of ODEs
Question Statement:
Using Euler's method with a step size of $h = 0.1$, find the value of $y(0.2)$ for the initial value problem $\frac{dy}{dx} = x + y$, with $y(0) = 1$.
Step-by-Step Solution & Explanation
Step 1: at $x_0 = 0, y_0 = 1$:
$f(x_0, y_0) = 0 + 1 = 1$
$y_1 = y_0 + h f(x_0, y_0) = 1 + (0.1)(1) = 1.1$
at $x_1 = 0.1$.
Step 2: at $x_1 = 0.1, y_1 = 1.1$:
$f(x_1, y_1) = 0.1 + 1.1 = 1.2$
$y_2 = y_1 + h f(x_1, y_1) = 1.1 + (0.1)(1.2) = 1.1 + 0.12 = 1.22$
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