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Author: SakshamJr

lab_01_bisection.cpp

@@ -0,0 +1,34 @@
+#include <iostream>
+#include <cmath>
+#define f(x) x *x *x + 3 * x *log10(x)
+#define e 0.000001
+
+using namespace std;
+int main()
+{
+    system("cls");
+    double a, b, c;
+    double fa, fb, fc;
+    cout << "Enter Intervals a and b: ";
+    cin >> a >> b;
+    do
+    {
+        fa = f(a);
+        fb = f(b);
+        if (fa * fb > 0)
+        {
+            cout << "Invalid Intervals! They donot Bracket the root!" << endl;
+            return 0;
+        }
+        c = (a + b) / 2;
+        fc = f(c);
+        if (fc * fa < 0)
+            b = c;
+        else if (fb * fc < 0)
+            a = c;
+        else 
+        cout << "ERROR!! \n";
+    } while (fabs((b-a)/a) > e);
+    cout << "Root = " << c << endl;
+    return 0;
+}

lab_02_newton_raphson.cpp

@@ -0,0 +1,22 @@
+#include <iostream>
+#include <cmath>
+#define e 0.000001
+#define f(x) cos(x) + x *x - 4
+#define fd(x) 2 * x - sin(x)
+using namespace std;
+int main()
+{
+    system("cls");
+    double x0, x = 0, fx0, fdx0;
+    cout << "Enter Initial Guess: ";
+    cin >> x0;
+    do
+    {
+        fx0 = f(x0);
+        fdx0 = fd(x0);
+        x = x0 - (fx0 / fdx0);
+        x0 = x;
+    } while (fabs(f(x)) > e);
+    cout << "Root = " << x;
+    return 0;
+}

lab_02_secantmethod.cpp

@@ -0,0 +1,24 @@
+#include <iostream>
+#include <cmath>
+#define e 0.0001
+#define f(x) x*x-3*x*log(x)
+using namespace std;
+int main()
+{
+    system("cls");
+    double a, b, c, fa, fb, fc;
+    int iterations;
+    cout << "Enter Initial Guesses a and b: ";
+    cin >> a >> b;
+    do
+    {
+        fa = f(a);
+        fb = f(b);
+        c = (a * fb - b * fa) / (fb - fa);
+        fc = f(c);
+        a = b;
+        b = c;
+    } while (fabs(fc) > e);
+    cout << "Root: " << c;
+    return 0;
+}

lab_03_gauss_elimination.cpp

@@ -0,0 +1,56 @@
+#include <iostream>
+using namespace std;
+
+int main()
+{
+    int n, i, j, k;
+    cout << "Enter number of unknowns: ";
+    cin >> n;
+
+    float a[n][n + 1], x[n], ratio;
+
+    cout << "Enter Coefficients of Augmented Matrix: " << endl;
+    for (i = 0; i < n; i++)
+        for (j = 0; j < n + 1; j++)
+            cin >> a[i][j];
+
+    /* Gaussian Elimination */
+    for (i = 0; i < n - 1; i++)
+    {
+        if (a[i][i] == 0.0)
+        {
+            cout << "Mathematical Error!";
+            return 0;
+        }
+        for (j = i + 1; j < n; j++)
+        {
+            ratio = a[j][i] / a[i][i];
+            for (k = 0; k <= n; k++)
+            {
+                a[j][k] = a[j][k] - ratio * a[i][k];
+            }
+        }
+    }
+
+    /* Back Substitution */
+    x[n - 1] = a[n - 1][n] / a[n - 1][n - 1];
+    for (i = n - 2; i >= 0; i--)
+    {
+        x[i] = a[i][n];
+        for (j = i + 1; j < n; j++)
+        {
+            x[i] -= a[i][j] * x[j];
+        }
+        x[i] = x[i] / a[i][i];
+    }
+
+    /* Display Solution */
+    cout << endl
+         << "Solution: " << endl;
+    for (i = 0; i < n; i++)
+    {
+        cout << "x[" << i + 1 << "] = " << x[i] << endl;
+    }
+
+    return 0;
+}

lab_03_gauss_jordan.cpp

@@ -0,0 +1,48 @@
+#include <iostream>
+
+using namespace std;
+int main()
+{
+    system("cls");
+    int size, i, j, k;
+    cout << "Enter Size of a: ";
+    cin >> size;
+    float a[size][size + 1], x[size];
+    float ratio;
+    cout << "Enter Coefficients of Augmented a: ";
+    for (i = 0; i < size; i++)
+    {
+        for (j = 0; j < size + 1; j++)
+        {
+            cin >> a[i][j];
+        }
+    }
+
+    // Calculating the Identity a
+    for (i = 0; i < size; i++)
+    {
+        if (a[i][i] == 0)
+        {
+            cout << "Gauss Jordan Method Fails! ";
+            exit(0);
+        }
+        for (j = 0; j < size; j++)
+        {
+            if (i != j)
+            {
+                ratio = a[j][i] / a[i][i];
+                for (k = 0; k < size + 1; k++)
+                    a[j][k] -= ratio * a[i][k];
+            }
+        }
+    }
+
+    // Assigning and Displaying the Result
+    for (i = 0; i < size; i++)
+    {
+        x[i] = a[i][size] / a[i][i];
+        cout << "x" << i << " = " << x[i] << endl;
+    }
+
+    return 0;
+}

lab_04_EulersMethod.cpp

@@ -0,0 +1,34 @@
+/*Solution of First Order Ordinary Differential Equation*/
+// Also called Initial Value Problem
+// Approximate Value is found out
+
+#include <iostream>
+#include <cmath>
+#include <iomanip>
+#define f(x, y) 6 * x - 3
+using namespace std;
+int main()
+{
+    system("cls");
+    float x0, y0, x1, y1, xn, h, s;
+    cout << "Enter x0 and y0: ";
+    cin >> x0 >> y0;
+    cout << "Enter xn: ";
+    cin >> xn;
+    cout << "Enter incremental value: ";
+    cin >> h;
+    cout << "Solution: \n\n";
+    cout << "  x\t  y\n";
+    cout << "---------------\n";
+    cout << setw(4) << x0 << "\t" << setw(6) << y0 << endl;
+    while (x0 < xn)
+    {
+        s = f(x0, y0);
+        x1 = x0 + h;
+        y1 = y0 + h * s;
+        x0 = x1;
+        y0 = y1;
+        cout << setw(4) << x0 << "\t" << setw(6) << y0 << endl;
+    }
+    return 0;
+}

lab_04_Inverse_GJordan.cpp

@@ -0,0 +1,65 @@
+#include <iostream>
+#include <iomanip>
+using namespace std;
+int main()
+{
+    system("cls");
+    int size, i, j, k;
+    cout << "Enter no. of Unknowns: ";
+    cin >> size;
+    float a[size][size], inv[size][size], ratio;
+
+    /*Initializing Identity Matrix*/
+    for (i = 0; i < size; i++)
+    {
+        for (j = 0; j < size; j++)
+        {
+            if (i == j)
+                inv[i][j] = 1;
+            else
+                inv[i][j] = 0;
+        }
+    }
+
+    /*Input the Matrix to be Inversed*/
+    cout << "Enter Matrix to be Inversed: ";
+    for (i = 0; i < size; i++)
+        for (j = 0; j < size; j++)
+            cin >> a[i][j];
+
+    /*Gauss Jordan Method*/
+    for (i = 0; i < size; i++)
+    {
+        if (a[i][i] == 0)
+        {
+            cout << "Diagonal Element Cannot Be Zero!";
+            exit(0);
+        }
+        for (j = 0; j < size; j++)
+        {
+            ratio = a[j][i] / a[i][i];
+            if (i != j)
+            {
+                for (k = 0; k < size; k++)
+                {
+                    a[j][k] -= ratio * a[i][k];
+                    inv[j][k] -= ratio * inv[i][k]; // simultaneously applying row transformation to the identity matrix
+                }
+            }
+        }
+    }
+
+    /*Display the Inverse*/
+    cout << endl
+         << "Inverse of Matrix is: " << endl;
+    for (i = 0; i < size; i++)
+    {
+        for (j = 0; j < size; j++)
+        {
+            inv[i][j] /= a[i][i];
+            cout << setw(5) << inv[i][j] << "\t";
+        }
+        cout << endl;
+    }
+    return 0;
+}

lab_04_RK4_Method.cpp

@@ -0,0 +1,48 @@
+/*Solution of First Order Ordinary Differential Equation*/
+// Also called Initial Value Problem
+// Approximate Value is found out
+// yi+1 = yi + h*f(xi,yi)
+// Tabular form output
+// define f(x,y)
+// Input x0,y0,h,xn
+// s =f(x0,y0)
+// y1 = y0 + h * s
+// x1 = x0 + h
+// x0 = x1
+// y0 = y1
+// print in tablular form
+
+#include <iostream>
+#include <cmath>
+#include <iomanip>
+#define f(x, y) 6*x - 3
+using namespace std;
+int main()
+{
+    system("cls");
+    float x0, y0, x1, y1, xn, h, m1, m2, m3, m4, m;
+    cout << "Enter x0 and y0: ";
+    cin >> x0 >> y0;
+    cout << "Enter xn: ";
+    cin >> xn;
+    cout << "Enter incremental value: ";
+    cin >> h;
+    cout << "Solution: \n\n";
+    cout << "  x\t  y\n";
+    cout << "---------------\n";
+    cout << setw(4) << x0 << "\t" << setw(6) << y0 << endl;
+    while (x0 < xn)
+    {
+        m1 = f(x0, y0);
+        m2 = f(x0 + h / 2, y0 + m1 * h / 2);
+        m3 = f(x0 + h / 2, y0 + m2 * h / 2);
+        m4 = f(x0 + h, y0 + m3 * h);
+        m = (m1 + 2 * m2 + 2 * m3 + m4) / 6;
+        x1 = x0 + h;
+        y1 = y0 + h * m;
+        x0 = x1;
+        y0 = y1;
+        cout << setw(4) << x0 << "\t" << setw(6) << y0 << endl;
+    }
+    return 0;
+}

lab_05_ExpCurveFitting.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+using namespace std;
+int main()
+{
+    system("cls");
+    int n, i;
+    float sumx = 0, sumlny = 0, sumxlny = 0, sumx2 = 0, a, b;
+    cout << "Enter Number of Data Points: ";
+    cin >> n;
+    float x[n], y[n];
+
+    // Enter Values of X and Y
+    cout << "Enter Values of x and y: " << endl;
+    for (i = 0; i < n; i++)
+        cin >> x[i] >> y[i];
+
+    // Calculate the Summations
+    for (i = 0; i < n; i++)
+    {
+        sumx += x[i];
+        sumlny += log(y[i]);
+        sumxlny += x[i] * log(y[i]);
+        sumx2 += x[i] * x[i];
+    }
+
+    if ((sumx * sumx - sumx2 * n) != 0)
+    {
+        b = (sumlny * sumx - sumxlny * n) / (sumx * sumx - sumx2 * n);
+        a = (sumx * sumxlny - sumx2 * sumlny) / (sumx * sumx - sumx2 * n);
+        a = exp(a);
+        cout << "The Equation of Curve is: \n";
+        cout << fixed;
+        cout << "y = " << setw(5) << setprecision(4) << a << "e^" << setw(5) << b << "x";
+    }
+    else
+    {
+        cout << "Determinant is Zero!";
+        exit(0);
+    }
+    return 0;
+}