Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
Exercise 5.5 [Adam's Predictor and Corrector Method]
Solved Example Problems
Solve the following problems by 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 = 3ex + 2y with x0 =
0, y0 = 0 using Adams-Bashforth formula.
[Ans. y (0.4)= 2.20, y (0.5) = 3.20]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Solved Example Problems - Exercise 5.5 [Adam's Predictor and Corrector Method]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
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Statistics and Numerical Methods
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