PYQs Based Test - 28 : Numerical Methods (Differential Equations)

Error order of $3^{\mathrm{rd}}$ order Runge-Kutta method is

With a one unit change in 'b' what is the change in 'y' in the solution of the system of equations x + y = 2; 1.01x + 0.99y = b?

An explicit forward Euler method is used to numerically integrate the differential equation

$\frac{dy}{dt}=y$

using a time step of 0.1. With the initial condition y (0) = 1, the value of y (1) computed by this method is ___________ (correct to two decimal places).

Consider an ordinary differential equation. $\frac{\mathrm{dx}}{\mathrm{dt}}=4\mathrm{t}+4.$ If x = x₀ at t = 0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of Δt = 0.2 is

While numerically solving the differential equation $\frac{dy}{dx}+2x{y}^2=0,y\left(0\right)=1$ using Euler’s predictor corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is