Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
Exercise 5.1 [Taylor's Series Method]
Solved Example Problems
Using Taylor's Series method, solve the following problems.
EXERCISE 5.1 [Taylor's Series Method]
Using
Taylor's Series method, solve the following problems.
1.
Find y (0.2), y (0.4), given dy/dx = xy2 + 1, y (0) =1.
[Ans.
1.226, 1.5421]
2.010
Find y (0.1), given y' = x2y - 1, y (0) = 1
[Ans. 0.9003]
3.
Solve, y' = x + (1/10) y2, y (1.8) = 0, for y (2)
[Ans.
0.3809]
4.
Evaluate x (0.1), y (0.1), x (0.2), y (0.2), given dx/dt = ty + 1, dy/dt = -tx,
given x = 0, y = 1 at t = 0.
[Ans. 0.105, 0.9987, x (0.2) = 0.21998, y
(0.2) = 0.9972]
5.
Find y (0.1), y (0.2), y (0.3) given y' = (x3 + xy2)/ex,
y (0) = 1
[Ans. 1.0047, 1.01812, 1.03995]
6.
Find y (0.2), y (0.4), given y' = x - y2 and y (0) = 1
[Ans.
0.8511, 0.7751]
7.
Find y (0.2), y (0.4), given y'' + y = 0 given y (0) = 1, y' (0) = 0.
[Ans.
y (0.2) = 1.0204, y (0.4) = 1.0]
8.
Obtain the values of y at x= 0.1, 0.2, 0.3, if y satisfies
y''
= -xy and y (0) = 1, y' (0) 1, y'(0) = 0.5
[Ans.
1.0498, 1.0986, 1.145]
9.
Find y (0.4) if y' = 1 + xy, given y (0) = 2, taking h = 0.2
[Ans.
2.588419]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Solved Example Problems - Exercise 5.1 [Taylor's Series 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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