![Test the O(h) convergence theory of the composite Simpson method for the func- tion fx) - sin(x) cos(x) on [0, 1]. That is,](http://img.homeworklib.com/questions/38df73f0-aa86-11eb-b504-2736403206bd.png?x-oss-process=image/resize,w_560)
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Test the O(h') convergence theory of the composite Simpson method for the func- tion fx) -...
Use Matlab code Consider the following function sin(x) Using the following parameters in your functions: -func:...
Use
Matlab code
Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
help with 5 and 6? 5. Find the interval of convergence of .. A) O B)...
help with 5 and 6?
5. Find the interval of convergence of .. A) O B) 0 C) (0,00) I D) (-00,00) 6. Which of the following is an equation for the line tangent to the curve x = sin 38 cos , y = sin 30 sin 0 at 0 = */3? A) y = 732 B) y = 3x - C) y=for D) yr yr - 1
CAN YOU PLEASE CHECK WHATS WRONG? function[F]=func(t,h) global Atank Ahole kOne kTwo g rho %F=zeros(2,1) %NL=y(1)...
CAN YOU PLEASE CHECK WHATS WRONG? function[F]=func(t,h) global Atank Ahole kOne kTwo g rho %F=zeros(2,1) %NL=y(1) %NG=y(2) F=(kOne+kTwo*cos(2*pi*t/24)-rho*Ahole*sqrt(2*g*h))/(rho*Atank); close all clear all %clear all %close all global Atank Ahole kOne kTwo g rho Atank = 3.13;% Atank value Ahole =0.06; %Ahole value kOne = 300; % K1 value kTwo = 200; % K2 value g = 9.81; % Gravity rho = 1000; % rho value t0=0; tf=150; %range of time %Initial value h0_2=h(1); h0_1=h(2); h0_0=h(3); n=input('Enter the number of steps:');...
& The taylor series generated by fx)= et at a 9 is: B) ¿ (xaq) +!...
& The taylor series generated by fx)= et at a 9 is: B) ¿ (xaq) +! ni e (x-ght D o é (x-gin 1-0 (D+1)1 no (n+ ! I cos(x²) dx with an error less than o.ool is about: a) 0.9 6) 0.9046 c) Nore of the above ... 1492 3) The sum of the n n series 1 + 1 + 1 + 1 2 + I c) è se a) b) The sun of the series 1:1 +...
h 5. In Homework 8 we looked at the finite difference approximation of f'(x). f(x +...
h 5. In Homework 8 we looked at the finite difference approximation of f'(x). f(x + 1) = f(x) + f'(z)h + }}" (-x)+2 +0(h2). Rearranging terms, and dividing by h leads to D(h) f(x+h)-f(x) != f'(x) +}s"(x)h + O(n?). Find constants a and 8 such that A(h) = aD(h/2) + BD(h) = f'(x) + (h) (similar to convergence acceleration in Chapter 2, we are using our knowledge of the be- haviour of the error to get a better approximation!)...
Modify the given code below which uses Simpson's 3/8 method with 6 subintervals to answer the...
Modify the given code below which uses Simpson's 3/8 method with
6 subintervals to answer the question above.
if a==b
I=0
else
N=3;
h=(b-a)/N;
x=a:h:b;
y=Fun(x);
I=3*h/8*(y(1)+2*sum(y(4:3:(N-2)))+y(N+1));
N=2*N;
check=0;
% Calculating subsequent valus of I
while check==0;
h=(b-a)/N;
x=a:h:b;
y=Fun(x);
% Composite Simpson's 3/8 method, Eq. (9.22)
I_new=3*h/8*(y(1)+2*sum(y(4:3:(N-2)))+y(N+1));
I_new=I_new+3*h/8*3*(sum(y(2:3:(N-1)))+sum(y(3:3:N)));
% Compare solution with that calculated in the previous
iteration
error=abs((I-I_new)/I)*100; % (*)
if error>0.1 % continue iteration
check=0;
N=N*2;
I=I_new;
elseif error<=0.1 % end iteration
check=1;
I=I_new;
end
end
end...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a pow...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
Runge-Kutta method R-K method is given by the following algorithm. o y(xo)- given k2-f(xi5.yi tk,...
Runge-Kutta method R-K method is given by the following algorithm. Yo = y(xo) = given. k1-f(xy) k4-f(xi +h,yi + k3) 6 For i = 0, 1, 2, , n, where h = (b-a)/n. Consider the same IVP given in problem 2 and answer the following a) Write a MATLAB script file to find y(2) using h = 0.1 and call the file odeRK 19.m b) Generate the following table now using both ode Euler and odeRK19 only for h -0.01....
Of your choice. Draw a graph of fx) Problem: Apply various integration techniques to compute Note...
of your choice. Draw a graph of fx) Problem: Apply various integration techniques to compute Note the labsolute values!. Take f(0) to be: 2n divided by 6. 1. Obtain Trapezoidal estimate with one panel, Ti. Copy it in the table below. 2. Obtain Trapezoidal estimate with two panels, T. Copy it in the table. 3. Obtain Trapezoidal estimate with four panels, Ta. Copy it in the table. 4. Obtain Trapezoidal estimate with eight panels, Ts. Copy it in the table....
Instructions: Submit your script in a file named hwk08.m to the dropbox before 11:59 pm on the du...
Instructions: Submit your script in a file named hwk08.m to the dropbox before 11:59 pm on the due date NOTE: This assignment is neither quick nor simple. You will be well served to start on it early, and to ask for help if you need it. Being a more substantial assignment than earlier hwk, it is worth- s. When you ask your calculator for the value of a function for a specified argument, (e.g., sin(22), cos(74), In(6.5)), it almost certainly...
Use
Matlab code
Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
help with 5 and 6?
5. Find the interval of convergence of .. A) O B) 0 C) (0,00) I D) (-00,00) 6. Which of the following is an equation for the line tangent to the curve x = sin 38 cos , y = sin 30 sin 0 at 0 = */3? A) y = 732 B) y = 3x - C) y=for D) yr yr - 1
& The taylor series generated by fx)= et at a 9 is: B) ¿ (xaq) +! ni e (x-ght D o é (x-gin 1-0 (D+1)1 no (n+ ! I cos(x²) dx with an error less than o.ool is about: a) 0.9 6) 0.9046 c) Nore of the above ... 1492 3) The sum of the n n series 1 + 1 + 1 + 1 2 + I c) è se a) b) The sun of the series 1:1 +...
h 5. In Homework 8 we looked at the finite difference approximation of f'(x). f(x + 1) = f(x) + f'(z)h + }}" (-x)+2 +0(h2). Rearranging terms, and dividing by h leads to D(h) f(x+h)-f(x) != f'(x) +}s"(x)h + O(n?). Find constants a and 8 such that A(h) = aD(h/2) + BD(h) = f'(x) + (h) (similar to convergence acceleration in Chapter 2, we are using our knowledge of the be- haviour of the error to get a better approximation!)...
Modify the given code below which uses Simpson's 3/8 method with
6 subintervals to answer the question above.
if a==b
I=0
else
N=3;
h=(b-a)/N;
x=a:h:b;
y=Fun(x);
I=3*h/8*(y(1)+2*sum(y(4:3:(N-2)))+y(N+1));
N=2*N;
check=0;
% Calculating subsequent valus of I
while check==0;
h=(b-a)/N;
x=a:h:b;
y=Fun(x);
% Composite Simpson's 3/8 method, Eq. (9.22)
I_new=3*h/8*(y(1)+2*sum(y(4:3:(N-2)))+y(N+1));
I_new=I_new+3*h/8*3*(sum(y(2:3:(N-1)))+sum(y(3:3:N)));
% Compare solution with that calculated in the previous
iteration
error=abs((I-I_new)/I)*100; % (*)
if error>0.1 % continue iteration
check=0;
N=N*2;
I=I_new;
elseif error<=0.1 % end iteration
check=1;
I=I_new;
end
end
end...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
Runge-Kutta method R-K method is given by the following algorithm. Yo = y(xo) = given. k1-f(xy) k4-f(xi +h,yi + k3) 6 For i = 0, 1, 2, , n, where h = (b-a)/n. Consider the same IVP given in problem 2 and answer the following a) Write a MATLAB script file to find y(2) using h = 0.1 and call the file odeRK 19.m b) Generate the following table now using both ode Euler and odeRK19 only for h -0.01....
of your choice. Draw a graph of fx) Problem: Apply various integration techniques to compute Note the labsolute values!. Take f(0) to be: 2n divided by 6. 1. Obtain Trapezoidal estimate with one panel, Ti. Copy it in the table below. 2. Obtain Trapezoidal estimate with two panels, T. Copy it in the table. 3. Obtain Trapezoidal estimate with four panels, Ta. Copy it in the table. 4. Obtain Trapezoidal estimate with eight panels, Ts. Copy it in the table....
Instructions: Submit your script in a file named hwk08.m to the dropbox before 11:59 pm on the due date NOTE: This assignment is neither quick nor simple. You will be well served to start on it early, and to ask for help if you need it. Being a more substantial assignment than earlier hwk, it is worth- s. When you ask your calculator for the value of a function for a specified argument, (e.g., sin(22), cos(74), In(6.5)), it almost certainly...
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