Allied & ICAR Exam Bank • ALLIED_2778 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

For the IVP $\frac{dy}{dx} = -10 y$ with $y(0) = 1$, Euler's forward method is numerically stable if step size $h < k$. The value of $k$ is:

Answer Key:

0.2

Step-by-Step Solution & Explanation

Stability of Euler's method requires $|1 + h \lambda| < 1$. For $\lambda = -10$: $|1 - 10h| < 1 \implies -1 < 1 - 10h < 1 \implies 0 < 10h < 2 \implies h < 0.2$.
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