Engineering Mathematics - Numerical Methods

The ordinary differential equation $\frac{dy}{dt} = -\pi y$ subject to an initial condition $y(0) = 1$ is solved numerically using the following scheme: $\frac{y(t_{n+1}) - y(t_n)}{h} = -\pi y(t_n)$ where $h$ is the time...

Find the positive real root of x³ - x - 3 = 0 using Newton-Raphson method. If the starting guess (x₀) is 2, the numerical value of the root after two iterations (x₂) is ________ (round off to two decimal places).

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...