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find the minimum number of intervals required to evaluate integration 0 to 1 e^-xdx with an accuracy of 1/2 X 10^-4, by using the trapezoidal rule.
the solution of the system of equations (1 2, 2 1) (x, y) = (4, -2) is attempted by the Gauss Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the iteration schemes converge? Justify your answer.
Write down only one application of Runge Kutta Method to solve some real world problem.
Write down Runge Kutta Fehlberg Method(Error Control)
Determine the direction in which the scalar field
φ( x, y) = xy^2 + x^3y increases the
fastest at the point (1, 2).
φ( x, y) = xy^2 + x^3y increases the
fastest at the point (1, 2).
find the minimum number of intervals required to evaluate integartion 0 to 1 e^-x^2 dx woth an accuracy of 1/2 X 10^-4 by using trapezoidal rule
obtain an approximate value of integration 0 to 1 dx/1+x^2 using composite simpsons rule with h= 0.25 and h=0.125. Find also the improves value using Romberg's integration.
solve the system of equations
2x1 +3x2 +4x3 +x4 =3
x1 +2x2 +x4 =2
2x1 +3x2 +x3 -x4 =1
x1 -2x2 -x3 +4x4 =5
using Gauss elimination method with pivoting.
2x1 +3x2 +4x3 +x4 =3
x1 +2x2 +x4 =2
2x1 +3x2 +x3 -x4 =1
x1 -2x2 -x3 +4x4 =5
using Gauss elimination method with pivoting.
solve the following linear system ax=b of equation with partial pivoting
x1 -x2 +3x3 =3
2x1 +x2 +4x3 =7
3x1 + 5x2 -2x3 =6
Store the multipliers and also write the pivoting vectors.
x1 -x2 +3x3 =3
2x1 +x2 +4x3 =7
3x1 + 5x2 -2x3 =6
Store the multipliers and also write the pivoting vectors.
A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested
for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected
by a technician:
o Gas volume: V = 0.8 m 3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done = 2
1
V
V
pdV
i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m 3 to 0.6 m 3 using:
o integral calculus
o Simpson’s rule
o the mid-ordinate rule.
iii. Comment on the accuracy of the two numerical methods.
for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected
by a technician:
o Gas volume: V = 0.8 m 3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done = 2
1
V
V
pdV
i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m 3 to 0.6 m 3 using:
o integral calculus
o Simpson’s rule
o the mid-ordinate rule.
iii. Comment on the accuracy of the two numerical methods.
