Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
Exercise 5.2 [Euler and Modified Euler]
Solved Example Problems
Statistics and Numerical Methods : Unit - V : Numerical solution of ordinary differential Equations : Exercise 5.2 [Euler and Modified Euler]
EXERCISE 5.2 [Euler and Modified Euler]
1.
Use Euler's method to find y (0.4) given y' = xy, y (0) = 1.
[Ans.
1.0611]
2.
Use Modified Euler's method and obtain y (0.2) given
dy/dx
= log (x + y), y (0) = 1, h = 0.2
[Ans.
y (0.2) = 1.0095]
3.
Using modified Euler's method, get y (0.2), y(0.4), y (0.6) given
dy/dy
= y - x2, y (0) = 1.
[Ans. 1.218, 1.467, 1.737]
4.
Using modified Euler's method, solve dy/dx = y + x2, y(0) = 1 to find y (0.2)
and y (0.4) correct to 3 decimals.
[Ans.
y (0.2) = 1.24, y (0.4) = 1.514]
noiteups
sdt 01 (50) y hort
5.
Given dy/dx – x2 – y = 4, y(0) = 1. Determine y (0.02), y (0.04) and
y (0.06) using Euler's modified method.
[Ans. y (0.02) 1.0202, y (0.04) = 1.0408, y
(0.06) = 1.0619]
6.
Solve, dy/dx = 2y / x + x3 to obtain y (1.2) and y (1.4) given y =
0.5, when x = 1 by modified Euler's method.
[Ans. y (1.2) = 1.0228, y (1.4) = 1.8847]
7.
Using modified Euler's method solve the differential equation
dy/dx
+ y/x = y2 given that y = 1 when x = 1. Choose the step length 0.1.
Find y at x = 16.
[Ans.
y (1.6) = 1.1766]
8.
Given = dy/dx x + y2 and y (0) = 1. Find an approximate value of y
at x = 0.5 by modified Euler's method. Taking h = 0.1
[Ans. y (0.5) = 2.2070]
9.
Given dy/dx = x – y / x + y y(2) =1 Find y (1) by taking h = -0.2 using Euler's modified method.
[Ans. y (1) = 0.73207]
10.
Solve, dy/dx = x √1 + y2, y(1) = 0 at x = 3 taking h = 0.4 using Euler's
modified method.
[Ans.
y (3) = 21.671]
11.
Given dy/dx = y/x – (5/2) x2 y3, y(1) = 1 / √2 .Find y
(2) with h = 0.125 using Euler's modified method.
[Ans.
y (1) = 0.34939]
12.
Solve the differential equation dy / dx = -xy2, y (0) = 2 by
modified
Euler's
method and obtain y (0.2) by taking h = 0.1
[Ans.
y (0.2) = 1.9227]
13.
Solve dy/dx = 1 - y with y (0) = 0 at x = 0.1, 0.2, 0.3 using modified Euler's
method.
[Ans. y (0.1) = 0.095, y (0.2) = 0.1890, y
(0.3) = 0.2587]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Solved Example Problems - Exercise 5.2 [Euler and Modified Euler]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
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Statistics and Numerical Methods
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