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GATE Engineering Mathematics: Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods – Previous Year Questions

5 GATE previous year questions on Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods (Engineering Mathematics, Mechanical Engineering) with answers and explanations, from every paper.

  1. GATE 2023 ME Q50 (2 marks, Numerical answer) – The initial value problem dydt + 2y = 0, y(0) = 1 is solved numerically using the forward Euler's method with a constant and positive time step of t.…
  2. GATE 2024 ME Q11 (1 mark, Multiple choice) – In order to numerically solve the ordinary differential equation dydt = -y for t > 0, with an initial condition y(0) = 1, the following scheme is…
  3. GATE 2025 ME Q31 (1 mark, Numerical answer) – The values of a function f obtained for different values of x are shown in the table below. x 0 0.25 0.5 0.75 1.0 --- --- --- --- --- --- f(x) 0.9 2.0…
  4. GATE 2026 ME Q14 (1 mark, Multiple choice) – Newton-Raphson method for solving algebraic equations is based on
  5. GATE 2026 ME Q15 (1 mark, Multiple choice) – The exact solution of 04 dx1 + x is represented as n. If m represents numerically evaluated value of the above integral using Trapezoidal rule by…