IGNOU MTE 10 2018 - Using the classical R-K method of o(h4) calculate approximate solution

Question

Using the classical R-K method of o(h⁴) calculate approximate solution of the IVP, y' = 1− x + 4y, y(0) = 1 at x = 0.6, taking h = 0.1 and 0.2 . Use extrapolation technique to improve the accuracy.

14 Feb 2018

Answer :

Word Count : 267

To solve the initial value problem \( y' = 1 - x + 4y \), with \( y(0) = 1 \), at \( x = 0.6 \), using the classical Runge-Kutta method of order \( o(h^4) \), we will apply the following steps: ### Steps: 1. Classical 4th-order Runge-Kutta Method (RK4): The RK4 method is given by: \[ k_1 = h \cdot f(x_n, y_n) \] \[ k_2 = h \cdot f\left(x_n + \frac{h}{2}, y_n +

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