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List of top Numerical Analysis Questions on Numerical solutions of first order differential equations by explicit Euler's method asked in GATE MA

The initial value problem \[ \frac{dy}{dt} = f(t, y), t > 0, y(0) = 1, \] where \( f(t, y) = -10 y \), is solved by the following Euler method: \[ y_{n+1} = y_n + h f(t_n, y_n), n \geq 0, \text{with step-size} \, h. \] Then \( y_n \to 0 \) as \( n \to \infty \), provided
  • GATE MA - 2021
  • GATE MA
  • Numerical Analysis
  • Numerical solutions of first order differential equations by explicit Euler's method