exp 11: init

Signed-off-by: Amneesh Singh <natto@weirdnatto.in>

file.org

@@ -266,6 +266,7 @@ int main() {
 #+end_src
 
 #+LATEX: \clearpage
+
 * Program for solving numerical integration by Simpson's 3/8 rule.
 #+ATTR_LATEX: :options frame=single,breaklines=true
 #+begin_src C  :tangle 8.c :results output :exports both :wrap src text
@@ -297,65 +298,6 @@ int main() {
 }
 #+end_src
 
-* Program for finding inverse of linear equations using Gauss Jordan method.
-#+ATTR_LATEX: :options frame=single,breaklines=true
-#+begin_src C  :tangle 9.c :results output :exports both :wrap src text
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-double **inverse(double **matrix, int order) {
-  double **inverse = calloc(order, sizeof(double *));
-  for (int i = 0; i < order; i++) {
-    inverse[i] = calloc(2 * order, sizeof(double));
-    inverse[i][order + i] = 1;
-    memcpy(inverse[i], matrix[i], order * sizeof(double));
-  }
-
-  for (int i = 0; i < order; i++) {
-    for (int j = 0; j < order; j++) {
-      if (i == j)
-        continue;
-      double r = inverse[j][i] / inverse[i][i];
-
-      for (int k = 0; k < order * 2; k++)
-        inverse[j][k] -= r * inverse[i][k];
-    }
-  }
-
-  for (int i = 0; i < order; i++) {
-    for (int j = 0; j < order; j++)
-      inverse[i][j + order] /= inverse[i][i];
-  }
-
-  return inverse;
-}
-
-int main() {
-  const int ORDER = 3;
-
-  double **matrix = malloc(ORDER * sizeof(double *));
-  for (int i = 0; i < ORDER; i++)
-    matrix[i] = malloc(ORDER * sizeof(double));
-
-  matrix[0][0] = 92, matrix[0][1] = 4.5, matrix[0][2] = 61; // 92x + 4.5y + 61z = 0
-  matrix[1][0] = -2, matrix[1][1] = 0, matrix[1][2] = 92387; // -2x + 92387z = 0
-  matrix[2][0] = -2, matrix[2][1] = 0, matrix[2][2] = -23; // -2x - 23z = 0
-
-  double **inv = inverse(matrix, ORDER);
-
-  for (int i = 0; i < ORDER; i++) {
-    for (int j = 0; j < ORDER; j++)
-      printf("%lf ", inv[i][j + ORDER]);
-    printf("\n");
-    free(inv[i]);
-    free(matrix[i]);
-  }
-  free(inv);
-  free(matrix);
-}
-#+end_src
-
 #+LATEX: \clearpage
 
 * Program for finding inverse of linear equations using Gauss Jordan method.
@@ -483,3 +425,38 @@ int main() {
   free(matrix);
 }
 #+end_src
+
+#+LATEX: \clearpage
+
+* Program for solving ordinary differential equation using Renge Kutta method.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C  :tangle 11.c :results output :exports both :wrap src text
+#include <stdio.h>
+
+double f(double x, double y) { return (y * y - x) / (y + x * y * y); };
+
+double rungen_kutta_4(double x0, double y0, double xn, int steps) {
+  double h = (xn - x0) / steps;
+
+  while (steps--) {
+    double k1 = f(x0, y0) * h;
+    double k2 = f(x0 + h / 2, y0 + k1 / 2) * h;
+    double k3 = f(x0 + h / 2, y0 + k2 / 2) * h;
+    double k4 = f(x0 + h, y0 + k3) * h;
+
+    double k = (k1 + k4 + 2 * (k2 + k3)) / 6;
+
+    x0 += h, y0 += k;
+  }
+
+  return y0;
+}
+
+int main() {
+  double x0 = 0, y0 = 5, xn = 1784;
+  int steps = 1000000;
+
+  printf("Value of y at x=%0.4lf is y=%0.4lf", xn,
+         rungen_kutta_4(x0, y0, xn, steps));
+}
+#+end_src