MTH603 Quiz 4 Updated Sep 2022 by Attiq Kundi

MTH-603 Final-Term BY Attiq Kundi · “Knowledge For Us” · For More Solutions · (Updated at 09-09-2022)

1. Trapezoidal rule of integration of a define integral is of

O(h2)

2. In multistep method, if we choose small step size

Increase

3. tabular function but give more error
4. dy/dx=t+ h=0.2

1.2

initial condition y0=1 at t0=0 using modified Euler’s method, for the range 0≤t≤0.6

5. points the maximum value of 2nd derivative f(x)=-(2/x)

at x=4

6. dy/dx=t+y with initial condition y0=1 at t0=1 and h0=0.1 them k1 of RK

o.2

7. accuracy of trapezoidal and Simpson’s rule

Richardson’s extrapolation

method

8. Adam mouton also known as

Linear multistep

9. F(x) in the interval [a,b] gives

Area under f(x) on

[a,b]

10. dy/dx=t+ h=0.1

0.2

initial condition y0=1 at t0=0 find 2nd term in Taylor series when t=1, y’=0.2 and y

y

11. while employing trapezoidal and Simpson rules to evaluate the double integral numerically, by using trapezoidal and Simpson rule

plain region

12. dy/dt=1- initial condition y0=1 at t0=0 find 2nd term in Taylor series when t=0.5, y’=0
13. By the lines x=a, x=b, y=c, y=d we shall employ either trapezoidal or Simpson’s rule, variable at time

One

y

14. dy/dt=t+ y with the initial condition y0=1 at t0=1 find the 2nd term in Taylor series when t=1.5, y’=1.2

0.6

15. dy/dt=y-t/y=t with the initial condition y=1 at t=0 find the 3rd term in Taylor series when t=0, y’’=0.2

0.018

16. lead towards the numerical integration method

All above choice are true

17. Adams-Bashforth is a multistep method

True

18. To evaluate a define integral of tabular function f(x), linear approximate led to
19. points the minimum value of 2nd derivative f(x)=-(2/x)

at x=1

20. in Trapezoidal rule, subinterval o equal length using—points

n+1

21. in solving the differentiate equation by Euler’s method y(0.2) is calculate as

1.02

22. Adams method are superior if output at many point

True

23. K4 is

K4=hf(tn+h1yn+k3)

24. Yn+1=yn+1/6(k1+2 k2+2k3 +k4) is

Runge-Kutta’s formula

25. To evaluate a define integral of tabular function f(x), piecewise quadratic approximate led to

Simpson’s rule

26. F(x) in continuous on [a,b] and we divide [a,b]

even

27. dy/dx=y+x /y-x with initial condition y0=1 at x0=0 and h=0.2 them k2 of Runge-Kutta method

o.22

28. dy/dx=t+y with initial condition y0=1 at t0=1 find the 3rd Taylor series when t=1.5 and y’=1 and y’’=1.2

o.1

29. K3 is

K3=hf(tn+h/2,yn+k2/2)

30. trapezoidal and Simpson’s integration are just linera combination values

independent

31. the area of trapezoid is obtained by adding the area of