From 077e1aa9bb3a93efe1f5630cd4544a814b293822 Mon Sep 17 00:00:00 2001 From: Amneesh Singh Date: Tue, 27 Dec 2022 15:22:58 +0530 Subject: [PATCH] exp 11: init Signed-off-by: Amneesh Singh --- 11.c | 28 ++++++++++++++++ file.org | 95 +++++++++++++++++++++---------------------------------- file.pdf | Bin 122732 -> 121267 bytes 3 files changed, 64 insertions(+), 59 deletions(-) create mode 100644 11.c diff --git a/11.c b/11.c new file mode 100644 index 0000000..07aa025 --- /dev/null +++ b/11.c @@ -0,0 +1,28 @@ +#include + +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)); +} diff --git a/file.org b/file.org index 05c8b8e..5a87e0d 100644 --- a/file.org +++ b/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 -#include -#include - -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 + +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 diff --git a/file.pdf b/file.pdf index 2dfb8282719be5fe6faa2a6e683fbc855ae0723d..322b6aef093f3fabf5539ad21df30296b7959420 100644 GIT binary patch delta 38137 zcmaE}kA3rI_6;1D>WvI64eac=ic5-86LYyLZoQ2@+4tB?VDEG7FU)B>^baiHXPm@X zG?`dTsb3sp(OsyXsp)Y2c{Qm3q{I~sUSF2>o z`#HvER-yWWvdZ$F+v|)bJ#ttTqW4~1Tik1b^|CpU7yQl!*Phe4!FxG@XMb(XzS{HK z9;zuu7`Un3o)F;d%YJ%?*iE}d3IRLU&pAC^MWp+Dz`7JcKU14$S02T)sH)!IulLHU zzW2?KFZ$P1Rn=#@Jbt?CpFUd` zPt(=R-gjg}!O8+&Sz(U#H`eQ0Y+G~u_&!Cun(F&CtJX!8@^8(y6+WiFb#^8X?}}|1 zf$b7{>!-bD;EvwujtXj!(BtRSaBoz5cIBJ7*hD!X`(j zmaV&2@y&7F!4@gIesg&2`iR0hTiKAna~Y;0(fN0rd9$wXay%FqwJNqMQ@1B+*}?Y0 z`rC0$@hmr^1laDrj`{E?uIcj@qitocf1F~T5WZHUa7SpmlHl3l%Y>aywE;<=q&(_s)Q{|9km+3N z-=XoX*O_ngy{#G7{pDEG?c5BU)~~sKV=c2s?`hsUdXAgivR7%=-mZGQG*YRi>7?gs zhn-0`7pTnGvNBZKcke5SPaJozOl)mxKWprLqTb8rxxLBOJ)+KD$Cg^FpWtp)R*6{m 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