Приложение 2. Листинг программы «Метод конечных разностей»

#include "stdafx.h"

#include "math.h"

const int N_max=200;

const double epsel=0.00001;

const double a=1.3, b=1.8, A=2.2, B=-1.4;

double F(double x)

{ return 1.8/(x*x)-4;}

double Q(double x)

{ return 2.3/x;}

double P(double x)

{ return 0.9*x;}

void Metod_K_R(double y[],double h,int n )

{int i;

double x,m,k,f;

static double c[N_max],d[N_max];

c[0]=0;

d[0]=A;

for( i=1;i<n;i++)

{

x=a+i*h;

m=(Q(x) - 2/(h*h)) / (1/(h*h) + P(x)/(2*h));

k= (1/(h*h) - P(x)/(2*h)) / (1/(h*h) + P(x)/(2*h));

f=F(x) / (1/(h*h) + P(x)/(2*h));

c[i]=1/(m-k*c[i-1]);

d[i]=c[i]*(f-k*d[i-1]);

}

y[n]=B;

for(i=n-1;i>=0;i--)

y[i]=d[i]-c[i]*y[i+1];

}

double Prov_toch(double y[],double y_tochnoe[],int n,double delta,double eps[])

{

int i;

delta=0;

for(i=0;i<=n/2;i++)

{

eps[i]=fabs(y[2*i]-y_tochnoe[i]);

if(eps[i]>delta)

delta=eps[i];

}

return delta;

}

void Pechat(double y_vivodimoe[],double a,double eps[],int n,int N,double delta)

{

int i,j=1,k;

double h,x=a;

k=n/N;

h=(b-a)/n;

printf("n = %d\nh = %1.2f\nMax_Delta = %1.2e\n\n",n,h,delta);

printf("\tx\ty\t\tE\n");

for(i=0;i<=n;i+=k)

{

printf("%d)\t%1.2f\t%f\t%1.2e\n",j++,x,y_vivodimoe[i],eps[i]);

x=x+k*h;

}

}

main()

{

int i,N=25,n;

double y[N_max],y_tochnoe[N_max],eps[N_max],y_vivodimoe[N_max];

double h,delta;

n=N;

do

{

if(n>=N_max)

{

printf("Vihod za predeli masiva ");

return 0;

}

h=(b-a)/n;

Metod_K_R(y,h,n);

delta=Prov_toch(y,y_tochnoe,n,delta,eps);

for(i=0;i<=n;i++){

y_vivodimoe[i]=y_tochnoe[i];

y_tochnoe[i] = y[i];}

n=2*n;

}

while(delta>epsel);

Pechat(y_vivodimoe,a,eps,n/4,N,delta);

printf("n = %d\nh = %1.2f\nMax_Delta = %1.2e\n\n",n,h,delta);

return 0;}

Приложение 3. Листинг программы «Метод Галёркина»

#include "stdafx.h"

#include "math.h"

#include "process.h"

const double epsel=0.00001;

const double h=0.02;

const double a=1.3;

const double b=1.8;

const double A=2.2;

const double B=-1.4;

const int M=10, N_max=26, E=8;

double F(double x)

{ return 1.8/(x*x)-4;}

double Q(double x)

{ return 2.3/x;}

double P(double x)

{ return 0.9*x;}

void Resheniya(double D[],double C[],int n)

{

double U,L,matrix[N_max][N_max];

double x,sum1,sum2,h=(b-a)/E,koef;

int k,i,j,t;

for(k=1;k<=n;k++){

for(i=1;i<=n;i++)

{sum1=0;sum2=0;

for(j=1;j<E;j++)

{

x=a+j*h;

U=pow(x-a,i)*(x-b);

L=k*pow(x-a,k-2)*((k-1)*(x-b)+2*(x-a))+P(x)*(k*pow(x-a,k-1)*(x-b)+pow(x-a,k))+Q(x)*pow(x-a,k)*(x-b);

if(j%2) sum1+=U*L;

else sum2+=U*L;

}

matrix[i-1][k-1]=h/3*(4*sum1+2*sum2);

}

}

for(i=1;i<=n;i++)

{sum1=0;sum2=0;

for(j=1;j<E;j++)

{

x=a+j*h;

U=pow(x-a,i)*(x-b);

L=P(x)*(B-A)/(b-a)+Q(x)*((A*b-B*a)/(b-a)+(B-A)/(b-a)*x);

if(j%2) sum1+=U*(F(x)-L);

else sum2+=U*(F(x)-L);

}

D[i-1]=h/3*(4*sum1+2*sum2);

}

// Metod Gausa

for(t=0;t<n-1;t++)

{

for( i=t+1;i<n;i++){

koef=matrix[i][t]/matrix[t][t];

D[i]=D[i]-D[t]*koef;

for( j=t+1;j<n;j++){

matrix[i][j]=matrix[i][j]-matrix[t][j]*koef;

}

}

}

for(i=n-1;i>=0;i--){

C[i]=D[i];

for(j=i+1;j<n;j++)

{C[i]=C[i]- matrix[i][j]*C[j];}

C[i]=C[i]/matrix[i][i];}

}

void Nahozdenie_y(double y[],double C[],int n)

{

int i,j;

double x,m=(A*b-B*a)/(b-a),g=(B-A)/(b-a);

for(j=0;j<N_max;j++){

x=a+j*h;

y[j]=m+g*x;

for(i=1;i<=n;i++)

{y[j]+=C[i-1]*pow(x-a,i)*(x-b);}

}

}

double Proverka(double y[],double y_tekushee[],int n,double eps[])

{

int i;

double delta;

for(i=0;i<N_max;i++)

{eps[i]=fabs(y[i]-y_tekushee[i]);

if(eps[i]>delta)delta=eps[i]; }

return delta;

}

void Prisvoenie_y_tekushee(double y[],double y_tekushee[],double y_vivodimoe[],int n)

{

int i;

for(i=0;i<N_max;i++)

{y_vivodimoe[i]=y_tekushee[i];

y_tekushee[i] = y[i];}

}

void Pechat_rez(double y_vivodimoe[],double eps[], int n,double delta)

{ int i;

double x;

printf("Bazis = %d\n",n);

printf("Razbienij v metode Simpsona = %d \n",E);

printf("Max_Delta = %1.2e\n\n",delta);

printf("\t X\t Y(X)\t\t Delta\n");

for(i=0;i<N_max;i++)

{

x=a+i*h;

printf("\t %1.2f \t %lf \t %1.2e\n",x,y_vivodimoe[i],eps[i]);

}

}

main()

{

int n=0;

double y[N_max],y_tekushee[N_max],y_vivodimoe[N_max],eps[N_max],B[N_max],C[N_max];

double delta;

do

{

n++;

if(n>=M)

{

printf("Error!!! Vihod za predeli\n\n");

return 0;

}

Resheniya(B,C,n);

Nahozdenie_y(y,C,n);

delta=Proverka(y,y_tekushee,n,eps);

Prisvoenie_y_tekushee(y,y_tekushee,y_vivodimoe,n);

}while(delta>epsel);

Pechat_rez(y_vivodimoe,eps,n,delta);

return 0;

}

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