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Quantitative Methods
Write down Runge Kutta Fehlberg Method(Error Control)
Quantitative Methods
using sin(0.1)= 0.09983 and sin(0.2)= 0.19867, find an approximate value of sin(0.15) by using Lagrange's interpolation. Obtain a bound on the truncation error.
Quantitative Methods
The solution of the system of equations (1 2, 2 1)(x,y) =(4,-2) is attempt 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.
Quantitative Methods
Starting with x^(0)=[1 1 1]^T, find the dominant eigenvalue and corresponding eigenvector for the matrix A= [4 -1 1, 4 -8 1, -2 1 5] using the power mwthod
Quantitative Methods
show that ux =c1eax +c2e-ax is the solution of the difference equation ux +1-2 ux Cosha+ux-1 =0
Quantitative Methods
using finite difference, show that the data f(-3)=13, f(-2)=7,f(-1)=3,f(0)=1,f(1)=1,f(2)=3,f(3)=7. represents a second degree polynomial. obtain this polynomial using interpolation and find f(2.5).
Quantitative Methods
a table of values is to be constructed for the function f(x) =1 /1+x in the interval [1,4] with equal step length. determine the spacing h such that quadratic interpolation gives result with accuracy 1×10 - 6
Quantitative Methods
use modified euler 's method to find the approximate solution of IVP y' =2xy, y(1)=1, at x=1.5 with h=0.1. if the exact solution is y(x) =ex2-1, find the error.
Quantitative Methods
For h=0.5,. 25,.125 solve integration from 0 to 1, dx/1+x2 and improve the accuracy by romberg integration. Compare your value with the real value.
Quantitative Methods
derive a suitable numerical differentiation formula of 0(h2) to find f''(2. 4) with h =0.1 given the table f(0.1)=3.41, f(1.2) =2.68, f(2.4)=1. 37, f(3.9) =-1. 48.
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#340153 on Dec 2023
#340153 on Dec 2023