数值分析程序.docVIP

拉格朗日 #includeiostream #include cmath using namespace std; double func (double m); int main() { const int j=100; int nn=0; double x=0.0,y=0.0,temp=0; cout请输入要插节点个数endl; cinnn; cout请输入x的值:endl; cinx; double a[j],b[j]; for(int i=0;inn;++i) { cout请输入x的第i+1个值:; cina[i]; temp=a[i]; b[i]=func(temp); } for(int k=0;knn;++k) { double t=1.0; for(int n=0;nnn;++n) { if(k==n) ++n; if(n==nn) break; t=t*(x-a[n])/(a[k]-a[n]); } y=y+t*b[k]; } cout结果为:yendl; return 0; } double func (double m) { return sqrt(m) ; } 四阶龙格库塔 #includeiostream using namespace std; double g(double,double); double rungekutta(double x0,double y0,double h,double N); int main() { double x0,y0,h; int N; coutPlease input the beginning point x0, y0, step length h, calculating times N.endl; cinx0y0hN; coutrungekutta(x0,y0,h,N); } double rungekutta(double x0,double y0,double h,double N) { int i; double x1,y1,K1,K2,K3,K4; for(i=0;i!=N;i++) { x1=x0+h; K1=g(x0,y0); K2=g(x0+h/2,y0+h/2*K1); K3=g(x0+h/2,y0+h/2*K2); K4=g(x1,y0+h*K3); y1=y0+h/6*(K1+2*K2+2*K3+K4); x0=x1; y0=y1; } return y1; } //注：以下的函数需要根据实际情况进行调整 double g(double x,double y) { return y-2*x/y; } 快速弦截法 #includeiostream using namespace std; //下列函数的参数表按实际函数的不同定义 一般只需要x double h(double a,double b,double c,double x); int main() { double x,x1,x2,eps,n,a,b,c; int k=1; //此处求解的方程为a*x^2+b*x+c=0，根据情况改变 coutSolving Equation a*x^2+b*x+c=0, input a,b,c,x0,x1,iteration times N and precision Eps.\n; //根据函数本有的变量进行输入 一般只需要输入第一个起始点x 第二个起始点x1 次数n和精度eps cinabcxx1neps; while(k=n) { if(h(a,b,c,x1)-h(a,b,c,x)==0) { coutIteration Failed. Try other starting points.\n; return 0; } x2=x1-(x1-x)*h(a,b,c,x1)/(h(a,b,c,x1)-h(a,b,c,x)); if(x2-x1epsx1-x2eps) { coutThe solution is x=x2endl; return 0; } x=x1; x1=x2; ++k; } coutIteration Failed. Cannot be precise enough.\n; return 0; } //以下根据情况改变 一般只需要未知数x double h(double a,double b,double c,double x)//Equation ax^2+bx+c=0 { return