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‎Bisection_method.c

+55
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#include<stdio.h>
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#define f(x) (x*x*x-2*x-5)
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int main()
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{
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float x1,x2,x0;
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printf("Enter the value of x1:");
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scanf("%f",&x1);
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printf("f(x1)=%f\n",f(x1));
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printf("Enter the value of x2:");
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scanf("%f",&x2);
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printf("f(x2)=%f\n",f(x2));
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if((f(x1)*f(x2))<0)
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{
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for(int i=1;i<=4;i++)
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{
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printf("For %d approximation of root\n ",i);
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x0=(x1+x2)/2;
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printf("x0=%f\n",x0);
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printf("f(x0)=%f\n",f(x0));
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if(f(x0)>0)
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{
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if(f(x1)>0)
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{
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x1=x0;
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}
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if(f(x2)>0)
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{
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x2=x0;
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}
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}
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else if(f(x0)<0)
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{
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if(f(x1)<0)
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{
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x1=x0;
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}
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if(f(x2)<0)
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{
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x2=x0;
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}
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}
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else
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{
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printf("Invalid...");
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}
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printf("x1=%f\nx2=%f",x1,x2);
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}
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}
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else
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{
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printf("\nInvalid input.");
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}
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return 0;
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}

‎Euler's_method.c

+36
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#include<stdio.h>
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#define f(x,y) (x+y) //((y-x)/(y+x))
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int main()
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{
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float x0,y0,y,xrq,h,n;
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printf("Enter the initial value of x:");
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scanf("%f",&x0);
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printf("Enter the initial value of y:");
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scanf("%f",&y0);
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printf("Enter the value of x for which y required:");
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scanf("%f",&xrq);
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printf("Enter the number of steps:");
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scanf("%f",&n);
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h=(xrq-x0)/n; //h=interval width(size of each step)
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printf("Step length=%f",h);
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for(int i=0;i<n;i++)
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{
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if(x0<=xrq)
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{
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y=y0+(h*f(x0,y0));
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y0=y;
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x0=x0+h;
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printf("\nx%d=%f\n",(i+1),x0);
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printf("y%d=%f\n",(i+1),y0);
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}
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else
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{
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break;
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}
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}
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printf("\nThe value of y is %f at x=%f",y,x0);
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return 0;
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}

‎Gauss_Elimination_method.c

+47
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#include<stdio.h>
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int main()
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{
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int i,j,k,n;
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float A[20][20],ratio,x[10],sum=0;
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printf("Enter the order of the matrix:");
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scanf("%d",&n);
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printf("\nEnter the elements of the augmented matrix:");
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for(i=1; i<=n; i++)
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{
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for(j=1;j<=(n+1);j++)
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{
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printf("A[%d][%d]=",i,j);
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scanf("%f",&A[i][j]);
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}
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}
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for(j=1;j<=n;j++)
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{
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for(i=1;i<=n;i++)
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{
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if(i>j)
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{
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ratio=A[i][j]/A[j][j];
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for(k=1;k<=n+1;k++)
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{
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A[i][k]=A[i][k]-ratio*A[j][k];
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}
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}
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}
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}
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x[n]=A[n][n+1]/A[n][n];
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for(i=n-1;i>=1;i--)
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{
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sum=0;
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for(j=i+1;j<=n;j++)
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{
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sum=sum+A[i][j]*x[j];
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}
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x[i]=(A[i][n+1]-sum)/A[i][i];
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}
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printf("\nSolution:");
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for(i=1;i<=n;i++)
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{
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printf("\nx%d=%f\t",i,x[i]);
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}
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return(0);
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}

‎Gauss_Jordan_method.c

+47
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#include<stdio.h>
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#include<math.h>
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#define SIZE 10
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int main()
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{
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float a[SIZE][SIZE], x[SIZE], ratio;
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int i,j,k,n;
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printf("Enter number of unknowns: ");
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scanf("%d", &n);
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printf("Enter coefficients of Augmented Matrix:\n");
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for(i=1;i<=n;i++)
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{
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for(j=1;j<=n+1;j++)
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{
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printf("a[%d][%d] = ",i,j);
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scanf("%f", &a[i][j]);
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}
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}
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for(i=1;i<=n;i++)
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{
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if(a[i][i] == 0.0)
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{
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printf("Mathematical Error!");
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}
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for(j=1;j<=n;j++)
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{
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if(i!=j)
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{
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ratio = a[j][i]/a[i][i];
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for(k=1;k<=n+1;k++)
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{
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a[j][k] = a[j][k] - ratio*a[i][k];
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}
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}
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}
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}
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for(i=1;i<=n;i++)
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{
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x[i] = a[i][n+1]/a[i][i];
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}
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printf("\nSolution:\n");
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for(i=1;i<=n;i++)
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{
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printf("x[%d] = %0.3f\n",i, x[i]);
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}
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return(0);
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}

‎LU_factorization.c

+71
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#include<stdio.h>
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void main()
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{
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float a[10][10],l[10][10],u[10][10],z[10],x[10],b[10];
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int i,j,k,n;
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printf("\nEnter the size of the coefficient matrix: ");
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scanf("%d",&n);
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printf("Enter the elements row-wise: ");
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for(i=0;i<n;i++)
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for(j=0;j<n;j++)
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scanf("%f",&a[i][j]);
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printf("Enter the right hand vector: ");
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for(i=0;i<n;i++)
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scanf("%f",&b[i]);
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for(i=0;i<n;i++)
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l[i][1]=a[i][1];
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for(j=2;j<=n;j++)
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u[1][j]=a[1][j]/l[1][1];
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for(i=0;i<n;i++)
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u[i][i]=1;
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for(i=2;i<=n;i++)
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for(j=2;j<=n;j++)
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if(i>=j)
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{
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l[i][j]=a[i][j];
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for(k=1;k<=j-1;k++)
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l[i][j]-=l[i][k]*u[k][j];
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}
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else
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{
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u[i][j]=a[i][j];
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for(k=1;k<=j-1;k++)
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u[i][j]=-l[i][k]*u[k][j];
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u[i][j]/=l[i][i];
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}
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printf("\nThe lower triangular matrix L: \n");
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for(i=0;i<=n;i++)
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{
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for(j=0;j<n;j++)
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printf("%f ",l[i][j]);
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printf("\n");
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}
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printf("\nThe upper triangular matrix U: \n");
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for(i=0;i<=n;i++)
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{
47+
for(j=0;j<i;j++)
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printf(" ");
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for(j=i;j<n;j++)
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printf("%f ",l[i][j]);
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printf("\n");
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}
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z[1]=b[1]/l[1][1];
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for(j=1;i<n;i++)
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{
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z[i]=b[i];
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for(j=0;j<i-1;j++)
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z[i]-=l[i][j]*z[j];
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z[i]/=l[i][i];
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}
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x[n]=z[n];
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for(i=n-1;i>=0;i--)
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{
64+
x[i]=z[i];
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for(j=i+1;j<n;j++)
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x[i]-=u[i][j]*x[j];
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}
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printf("The solution is: ");
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for(i=0;i<n;i++)
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printf("%f ",x[i]);
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}

‎Langrange_Interpolation_method.c

+35
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1+
#include<stdio.h>
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int main(){
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int i,j,n,xr,x[100],y[100];
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float p,yr=0;
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printf("Enter the num of entries:");
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scanf("%d",&n);
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printf("Enter the values of x:\n");
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for(i=0;i<n;i++)
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{
10+
printf("\nx[%d]=",i);
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scanf("%d",&x[i]);
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}
13+
printf("Enter the values of y:\n");
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for(i=0;i<n;i++)
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{
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printf("\ny[%d]=",i);
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scanf("%d",&y[i]);
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}
19+
printf("Enter the values x for which you want to find y:");
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scanf("%d",&xr);
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for(i=0;i<n;i++)
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{
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p=1;
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for(j=0;j<n;j++)
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{
26+
if(i!=j)
27+
{
28+
p=p*(xr-x[j])/(x[i]-x[j]);
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}
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}
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yr=yr+p*y[i];
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}
33+
printf("for x=%d then y=%f",xr,yr);
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return 0;
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}

‎Newton's_Backward_interpolation.c

+50
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1+
#include<stdio.h>
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int fact(int);
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void main()
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{
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int n,i,j,ch=30;
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float arr[10][11],px=1,x,y,p,h;
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printf("\nEnter the no of data:");
8+
scanf("%d",&n);
9+
printf("\nEnter the data:");
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for(i=0;i<n;i++)
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{
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printf("\nX%d=",i+1);
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scanf("%f",&arr[i][0]);
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printf("\nY%d=",i+1);
15+
scanf("%f",&arr[i][1]);
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}
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for(j=2;j<=n;j++)
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{
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for(i=0;i<n-1;i++)
20+
arr[i][j]=arr[i+1][j-1]-arr[i][j-1];
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}
22+
printf("\nThe difference table");
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printf("\n\tX \tY");
24+
for(i=0;i<n-1;i++)
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printf("\t%c^%d",ch,i+1);
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for(i=0;i<n;i++)
27+
{
28+
printf("\n");
29+
for(j=0;j<n+1-i;j++)
30+
printf("\t%.4f",arr[i][j]);
31+
}
32+
printf("\nEnter the value of x for f(x)");
33+
scanf("%f",&x);
34+
h=arr[n-1][0]-arr[n-2][0];
35+
p=(x-arr[n-1][0])/h;
36+
y=arr[n-1][1];
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for(i=1;i<n;i++)
38+
{
39+
px=px*(p+(i-1));
40+
y=y+(arr[n-1-i][i+1]*px)/fact(i);
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}
42+
printf("\nthe value of f(x) at x=%f is %f",x,y);
43+
}
44+
int fact(int n)
45+
{
46+
int f=1,i;
47+
for(i=1;i<=n;i++)
48+
f=f*i;
49+
return f;
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}

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