Write a C++ program that calculates the derivative using three methods (the forw

Question

Write a C++ program that calculates the derivative using three methods (the forward derivative, backward derivative, and the centered derivative) of a function that is defined separately from the main() part of the code. Have the user specify the value of , but print out the results for different step sizes: 01, 0.01, 0.001, and 0.0001 Use this code to calculate the derivatives of ( and sinh r for three values of 0.0,1.5, and 10.0. Use the smallest step size of the centered derivative to define the "correct" value (this is assuming no round-off error, of course), and determine the percent accuracy of each method/step size. Note: do not compare your result to the analytic result!

Explanation / Answer

Refer the below code:

#include <bits/stdc++.h>

using namespace std;

typedef long long int ll;

typedef long double ld;

#define f(x) (x-1)*(x-1)*(x-1)*(x-1)

#define g(x) sinh(x)

ld base;

ld h1 = 0.1,h2=0.01,h3=0.001,h4=0.0001;

ld fd(ld d,ld h)

{

ld fd_f = (f(d+h) - f(d))/h;

// cout << setprecision(10) << fd_f << endl;

return fd_f;

}

ld bd(ld d,ld h)

{

ld bd_f = (f(d) - f(d-h))/h;

// cout << setprecision(10) << bd_f << endl;

return bd_f;

}

ld cd(ld d,ld h)

{

ld cd_f = (f(d+h) - f(d-h))/(2*h);

// cout << setprecision(10) << cd_f << endl;

return cd_f;

}

void calulate_derivative(ld x,ld h)

{

ld a,b,c;

a = fd(x,h);

b = bd(x,h);

c = cd(x,h);

cout << setprecision(10);

cout << "Step size: " << h << endl;

ld dif;

dif = abs(base - a);

cout << "Forward Derivative = " << a << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

dif = abs(base - b);

cout << "Backward Derivative = " << b << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

dif = abs(base - c);

cout << "Centered Derivative = " << c << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

}

void input(ld x)

{

cout << x << endl;

base = cd(x,h4);

calulate_derivative(x,h1);

calulate_derivative(x,h2);

calulate_derivative(x,h3);

calulate_derivative(x,h4);

}

ld fd_sinh(ld d,ld h)

{

ld fd_f = (g(d+h) - g(d))/h;

// cout << setprecision(10) << fd_f << endl;

return fd_f;

}

ld bd_sinh(ld d,ld h)

{

ld bd_f = (g(d) - g(d-h))/h;

// cout << setprecision(10) << bd_f << endl;

return bd_f;

}

ld cd_sinh(ld d,ld h)

{

ld cd_f = (g(d+h) - g(d-h))/(2*h);

// cout << setprecision(10) << cd_f << endl;

return cd_f;

}

void calulate_derivative_sinh(ld x,ld h)

{

ld a,b,c;

a = fd_sinh(x,h);

b = bd_sinh(x,h);

c = cd_sinh(x,h);

cout << setprecision(10);

cout << "Step size: " << h << endl;

ld dif;

dif = abs(base - a);

cout << "Forward Derivative = " << a << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

dif = abs(base - b);

cout << "Backward Derivative = " << b << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

dif = abs(base - c);

cout << "Centered Derivative = " << c << " Accuracy: " << 100 - abs(dif/base)*100 << endl;

}

void input_sinh(ld x)

{

cout << x << endl;

base = cd_sinh(x,h4);

calulate_derivative_sinh(x,h1);

calulate_derivative_sinh(x,h2);

calulate_derivative_sinh(x,h3);

calulate_derivative_sinh(x,h4);

}

int main()

{

ios_base::sync_with_stdio(false);

cin.tie(NULL);

ld x;

cout << "Derivative of (x-1)^4:" << endl;

cin >> x;

input(x);

input(0);

input(1.5);

input(10);

cout << "Derivative of sinh x:" << endl;

cin >> x;

input_sinh(x);

input_sinh(0);

input_sinh(1.5);

input_sinh(10);

return 0;

}

Here fd,bd,cd are functions for forward derivative,backward derivative and centered derivative respectively and functions with _sinh are for derivative of sinh(x).

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.