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Программы для решения нелинейных уравнений
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Текст заголовочного файла methods.h.
/*******************************************************************/
extern double F(double);
/******************************************************************/
/* Ôóíêöèÿ F (X), çàäàâàåìàÿ ïîëüçîâàòåëåì */
/******************************************************************/
#ifdef __NEWTON
extern double F1(double);
/******************************************************************/
/* Ïðîèçâîäíàÿ ôóíêöèè F (X), çàäàâàåìàÿ ïîëüçîâàòåëåì */
/******************************************************************/
#endif
double Round (double X,double Delta);
/******************************************************************/
/* Ôóíêöèÿ Round (X,Delta), ïðåäíàçíà÷åíà äëÿ îêðóãëåíèÿ */
/* X ñ òî÷íîñòüþ Delta */
/******************************************************************/
double BISECT(double Left,double Right,double Eps,int &N);
/******************************************************************/
/* Ôóíêöèÿ BISECT ïðåäíàçíà÷åíà äëÿ ðåøåíèÿ óðàâíåíèÿ F(X)=0 */
/* ìåòîäîì äåëåíèÿ îòðåçêà ïîïîëàì. Èñïîëüçîâàíû îáîçíà÷åíèÿ: */
/* Left - ëåâûé êîíåö ïðîìåæóòêà */
/* Right - ïðàâûé êîíåö ïðîìåæóòêà */
/* Eps - ïîãðåøíîñòü âû÷èñëåíèÿ êîðíÿ óðàâíåíèÿ; */
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/* N - ÷èñëî èòåðàöèé */
/******************************************************************/
double ITER(double X0,double Eps,int &N);
/******************************************************************/
/* Ôóíêöèÿ ITER ïðåäíàçíà÷åíà äëÿ ðåøåíèÿ óðàâíåíèÿ F(X)=X */
/* ìåòîäîì ïðîñòîé èòåðàöèè. Èñïîëüçîâàíû îáîçíà÷åíèÿ: */
/* X0 - íà÷àëüíîå ïðèáëèæåíèå êîðíÿ */
/* Eps - ïîãðåøíîñòü âû÷èñëåíèÿ êîðíÿ óðàâíåíèÿ; */
/* N - ÷èñëî èòåðàöèé */
/******************************************************************/
double HORDA(double Left,double Right,double Eps,int &N);
/******************************************************************/
/* Ôóíêöèÿ HORDA ïðåäíàçíà÷åíà äëÿ ðåøåíèÿ óðàâíåíèÿ F(x)=0 */
/* ìåòîäîì õîðä. Èñïîëüçîâàíû îáîçíà÷åíèÿ: */
/* Left - ëåâûé êîíåö ïðîìåæóòêà */
/* Right - ïðàâûé êîíåö ïðîìåæóòêà */
/* Eps - ïîãðåøíîñòü âû÷èñëåíèÿ êîðíÿ óðàâíåíèÿ; */
/* N - ÷èñëî èòåðàöèé */
/******************************************************************/
double NEWTON (double X,double Eps,int &N);
/******************************************************************/
/* Ôóíêöèÿ NEWTON ïðåäíàçíà÷åíà äëÿ ðåøåíèÿ óðàâíåíèÿ F(X)=0 */
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/* ìåòîäîì êàñàòåëüíûõ. Èñïîëüçîâàíû îáîçíà÷åíèÿ: */
/* X - íà÷àëüíîå ïðèáëèæåíèå êîðíÿ */
/* Eps - ïîãðåøíîñòü âû÷èñëåíèÿ êîðíÿ óðàâíåíèÿ; */
/* N - ÷èñëî èòåðàöèé */
/******************************************************************/
#include "methods.cpp"
/************************************************************************/
Текст программного модуля methods.cpp.
/*********************************************/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
extern double F(double);
double BISECT(double Left,double Right,double Eps,int &N)
{
double E = fabs(Eps)*2.0;
double FLeft = F(Left);
double FRight = F(Right);
double X = (Left+Right)/2.0;
double Y;
if (FLeft*FRight>0.0) {puts("Íåâåðíîå çàäàíèå èíòåðâàëà\n");exit(1);}
if (Eps<=0.0) {puts("Íåâåðíîå çàäàíèå òî÷íîñòè\n");exit(1);}
N=0;
if (FLeft==0.0) return Left;
if (FRight==0.0) return Right;
while ((Right-Left)>=E)
{
X = 0.5*(Right + Left); /* âû÷èñëåíèå ñåðåäèíû îòðåçêà */
Y = F(X);
if (Y == 0.0) return (X);
if (Y*FLeft < 0.0)
Right=X;
else
{ Left=X; FLeft=Y; }
N++;
};
return(X);
}
double Round (double X,double Delta)
{
if (Delta<=1E-9) {puts("Íåâåðíîå çàäàíèå òî÷íîñòè îêðóãëåíèÿ\n");exit(1);}
if (X>0.0) return (Delta*(long((X/Delta)+0.5)));
else return (Delta*(long((X/Delta)-0.5)));
}
double ITER(double X0,double Eps,int &N)
{
if (Eps<=0.0) {puts("Íåâåðíîå çàäàíèå òî÷íîñòè\n");exit (1);}
double X1=F(X0);
double X2=F(X1);
N = 2;
while((X1 - X2)*(X1 - X2) > fabs((2*X1-X0-X2)*Eps))
{
X0 = X1;
X1 = X2;
X2 = F(X1);
N++;
}
return(X2);
}
#ifdef __NEWTON
double NEWTON (double X,double Eps,int &N)
{
extern double F1 (double);
double Y,Y1,DX;
N=0;
do
{
Y = F(X);
if (Y==0.0) return (X);
Y1 = F1(X);
if (Y1==0.0) {puts("Ïðîèçâîäíàÿ îáðàòèëàñü â íîëü\n");exit(1);}
DX=Y/Y1; X=X-DX; N++;
}
while (fabs(DX)>Eps);
return (X);
}
#endif
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double HORDA(double Left,double Right,double Eps,int &N)
{
double FLeft = F(Left);
double FRight = F(Right);
double X,Y;
if (FLeft*FRight>0.0) {puts("Íåâåðíîå çàäàíèå èíòåðâàëà\n");exit(1);}
if (Eps<=0.0) {puts("Íåâåðíîå çàäàíèå òî÷íîñòè\n");exit(1);}
N=0;
if (FLeft==0.0) return Left;
if (FRight==0.0) return Right;
do
{
X = Left-(Right-Left)*FLeft/(FRight-FLeft);
Y = F(X);
if (Y == 0.0) return (X);
if (Y*FLeft < 0.0)
{ Right=X; FRight=Y; }
else
{ Left=X; FLeft=Y; }
N++;
}
while (fabs(Y) >= Eps);
return(X);
}
/*********************************************************/
Численное интегрирование
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