Exercise 5.5 [Adam's Predictor and Corrector Method]

EXERCISE 5.5 [Adam's Predictor and Corrector Method]

Solve the following problems by Adam's Predictor and corrector method.

1. Given y = y - x², y (0) = 1, y (0.2) = 1.1218, y (0.4) = 1.4682, y (0.6) 1.7379. Estimate y (0.8) by Adam-Bashforth method.

 [Ans. 2.0138]

2. Obtain the solution of y' = x² (1+ y), y (1) = 1 at x = 1.1, 1.2, 1.3 by any numerical method and estimate at x = 1.4 by Adam’s method.

 [Ans. 2.5751]

3. Solve y' = x² + y² - 2, using Milne's method and Adam's method at x = 0.3 given y (0) = 1. The values of y at x = -0.1, 0.1, 0.2 may be 0100computed by Taylor's series.

 [Ans. 0.6148]

4. Using Adam's method determine y (0.4) and y (0.5) correct to 3 decimals given that dy/dx = 0.5 xy and y (0), y (0.1), y (0.2) and y (0.3) have values 1.0, 1.0025, 1.0101 and 1.0228 respectively.

[Ans. y (0.4) = 1.046, y (0.5) = 1.070]

5. Given dy/dx =x2 - y, y (0) = 1 and y (0.1) = 0.90516, y (0.2) = 0.82127, y (0.3) 0.74918. Obtain the value of y (0.4) using Adam's method.

 [Ans. y (1.4) = 0.6987]

6. Find y (0.4) and y (0.5) from dy/dx = 3e^x + 2y with x₀ = 0, y₀ = 0 using Adams-Bashforth formula.

 [Ans. y (0.4)= 2.20, y (0.5) = 3.20]