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C PROGRAM FOR GAUSS JORDAN METHOD

// gauss jordan method #include<stdio.h> int main() { int i,j,k,n; float a[20][20],c,x[10],sum=0.0; printf("\nEnter the order of matrix: "); scanf("%d",&n); printf("\nEnter the elements of augmented matrix row-wise:\n\n"); for(i=1; i<=n; i++) { for(j=1; j<=(n+1); j++) { printf("a[%d][%d] : ", i,j); scanf("%f",&a[i][j]); } } for(j=1; j<=n; j++) { for(i=1; i<=n; i++) { if(i!=j) { c=a[i][j]/a[j][j]; for(k=1; k<=n+1; k++) { a[i][k]=a[i][k]-c*a[j][k]; } } } } x[n]=a[n][n+1]/a[n][n]; printf("Augmented matrix AB :\n"); for(i=1;i<=n;i++) { for(j=1;j<=(n+1);j++) { printf("%f\t",a[i][j]); } printf("\n"); } for(i=n-1; ...
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TAYLOR'S SERIES FOR e^x sin(X) cos(X)

//Taylors series to find e^x,sin nx,cos x #include<stdio.h> #include<math.h> #define PI 3.1415 float expx(int ,int); double sinnx(int , int); double cosnx(int , int); int fact (int ); int main() { int x,n,i; do{ printf("Enter option\n1.e^x\n2.sin nx\n3.cos nx\n4.exit\n"); scanf("%d",&i); switch(i) { case 1 :printf("Enter x and number of terms\n"); scanf("%d%d",&x,&n); printf("e^%d in (%d) number of terms in taylor's series = %4.4f\n",x,n,expx(x,n)); break; case 2 :printf("Enter degree and number of terms\n"); scanf("%d%d",&x,&n); printf("sin(%d) in (%d) number of terms in taylor's series = %f\n",x,n,sinnx(x,n)); break; case 3 :printf("Enter degree and number of terms\n"); scanf("%d%d",&x,&n); printf("cos(%d) in (%d) number of terms in taylor...
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C PROGRAM FOR GAUSS SEIDEL METHOD.

//Program to implement Gauss Seidel #include<stdio.h> #include<math.h> int main() { float a[20][20],x[20],e,big,temp,relerror,sum=0;//e=relative error int n,i,j,maxit,itr; printf("Enter the size of the equation\n"); scanf("%d",&n); for(i=0;i<n;i++) { printf("Enter the co-efficent of equation of %d and RHS\n",i); for(j=0;j<=n;j++) scanf("%f",&a[i][j]); } printf("Enter relative error and number of itereation:\n"); scanf("%f%d",&e,&maxit); for(i=0;i<n;i++) { printf("Enter initial approx value of x[%d]=\n",i); scanf("%f",&x[i]); x[i]=0; } for(itr=1;itr<=maxit;itr++) { printf("\n Iteration [%d]",itr); big=0; for(i=0;i<n;i++) { sum=0; for(j=0;j<n;j++) { if(i!=j) sum=sum+a[i][j]*x[j]; } temp=(a[i][n]-sum)/a[i][i]; printf("   x[%d]=%f",i,temp);...
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GAUSS JACOBI'S METHOD.

//Program to implement Gauss Jacobi #include<stdio.h> #include<math.h> int main() { float a[20][20],xold[20],xnew[20],e,big,temp,relerror,sum=0;           // e = error   maxit=max no. of iterations int n,i,j,maxit,itr; printf("Enter the size of the equation\n"); scanf("%d",&n); for(i=0;i<n;i++) { printf("Enter the co-efficent of equation of %d and RHS\n",i); for(j=0;j<=n;j++) scanf("%f",&a[i][j]); } printf("Enter relative error and number of itereation:\n"); scanf("%f%d",&e,&maxit); for(i=0;i<n;i++) { printf("Enter initial approx value of x[%d]=\n",i); scanf("%f",&xold[i]); xnew[i]=0; } for(itr=1;itr<=maxit;itr++) { printf("\n Iteration [%d]",itr); big=0; for(i=0;i<n;i++) { sum=0; for(j=0;j<n;j++) { if(i!=j) sum=sum+a[i][j]*xold[j]; } temp=(a[i][n]-sum)...
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EULER'S MODIFIED METHOD.

//progran to implement euler's modified method #include<stdio.h> #include<math.h> #define F(x,y) exp(x)+y //here change to desired function int main () { double x0,x1,y0,y1,y2,n,h; int i,j,k; printf("Enter x0,y0,h,xn values \n"); scanf("%lf%lf%lf%lf",&x0,&y0,&h,&n); x1=x0+h; for(j=1;x1<=n;j++) { i=0;k=0; y2=y0+(h*F(x1-h,y0)); printf("   y%d-0 = %.6lf \n ",j,y2); do{ k++; y1=y0+h/2*(F(x1-h,y0)+F(x1,y2)); printf("\nx=%.3lf => y%d-%d =%.6lf\n",x1,j,k,y1); if(fabs(y1-y2)<0.000001) { printf("\ny%d =%.5lf \n\n",j,y1); i=1; } else y2=y1; }while(i!=1); y0=y1; x1=x1+h; } return 0; }
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EULER'S METHOD .

//program to implement euler's method to solve a differential equation #include<stdio.h> float fun (float x, float y) { return x+y; } int main () { float x,y,h,xn,k; printf("Enter x0,y0,h,xn \n"); scanf("%f%f%f%f",&x,&y,&h,&xn); printf("\nx\ty\n"); while(x<xn) { k=h*fun(x,y); y+=k; x+=h; printf("%.3f\t%.3f\n",x,y); } }
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RUNGE-KUTTA 2nd ORDER METHOD.

//program to implement runge kutta method of 4th order #include<stdio.h> #include<math.h> double F (double x,double y) {   return (x+y)/x; } int main () { double x0,y0,y1,n,h,f,k1,k2,k3,k4; printf("Enter x0,y0,h,xn values \n"); scanf("%lf%lf%lf%lf",&x0,&y0,&h,&n); for(;x0<n;x0+=h) { f=F(x0,y0); k1=h*f; f=F(x0+h,y0+k1); k2=h*f; y1=y0+(k1+k2)/2; printf("\nk1=%.5lf\nk2=%.5lf\n",k1,k2); printf("y(%.5lf) = %.3lf",x0+h,y1); y0=y1; } }
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