Q2Advanced Engineering Mathematics I

Question

Use Milne's Method to obtain the solution of the equation $\frac{d y}{d x} = x - y^{2}$ at $x = 0.8$ and at $x = 1$ given that $y (0) = 0$ .

Answer 1

Given $y^{'} = x - y^{2}$ , $y (0) = 0$ . We need starter values at $x = 0.2, 0.4, 0.6$ to find the value at $0.8$ using Milne's method.

Since starter values are not given, they must first be calculated using Taylor Series or Runge-Kutta methods.

Once $y_{1}, y_{2}, y_{3}$ are obtained, apply Milne's predictor and corrector formulas.

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