IGNOU MPH 14 2026 - Derive the Runge-Kutta 2nd Order formula for the diffe

Question

Derive the Runge-Kutta 2nd Order formula for the differential equation

19 Jan 2026

Answer :

Word Count : 286

Consider the first-order ordinary differential equation dy/dx = f(x, y), with the initial condition y(x₀) = y₀. The aim of the Runge–Kutta second-order method is to obtain an approximation for y at xₙ₊₁ = xₙ + h that is accurate up to terms of order h². Expand the exact solution y(xₙ + h) in a Taylor series about xₙ: y(xₙ + h) = yₙ + h(dy/dx)ₙ + (h²/2)(d²y/dx²)ₙ + O(h³). Using dy/dx = f(x,

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