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methods.cpp
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methods.cpp
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#include <iostream>
#include<cmath>
#include<iomanip>
#include<vector>
using namespace std;
class Methods{
public:
double func(double x, double y){
//double eta=5, k=1, m=0.6,n=1;
//return eta*pow(y,m)-pow(y,n)*k;
//return x*y;
//return pow((y+x), 2);
return x+y;
}
void Euler(double a,double b,double h,double yO ) {
double n=(b-a)/h;
double X[(int)n];
double y[(int)n];
X[0]=a;
y[0]=yO;
for(int i=0; i<n; i++){
X[i+1]=X[i]+h;
y[i+1] = (y[i]+h*func(X[i],y[i]));
}
for (int j = 0; j <=n; ++j) {
printf("X = %.2f", X[j]);
cout<<"\tY = "<<y[j]<<endl;
}
}
void Runge_kutte(double a,double b, double h, double yO) {
double n=(b-a)/h;
double x[(int)n];
double y[(int)n];
double k1,k2,k3,k4;
x[0]=a;
y[0]=yO;
for(int i=0; i<n; i++){
x[i+1]=x[i]+h;
k1=h*func(x[i],y[i]);
k2=h*func(x[i]+h/2.0,y[i]+k1/2.0);
k3=h*func(x[i]+h/2.0, y[i]+k2/2.0);
k4=h*func(x[i]+h,y[i]+k3);
y[i+1]=y[i]+(k1+2*k2+2*k3+k4)/6;
}
for (int j = 0; j <=n; ++j) {
printf("X = %.2f", x[j]);
cout<<"\tY = "<<y[j]<<endl;
}
}
void Rkutm(double a,double b, double h, double yO,double e) {
const double n=100000;
double x[(int)n],y[(int)n];
double k1,k2,k3,k4,k5,R;
x[0]=a; y[0]=yO;
for(int k=0; k<n; k++){
x[k+1]=x[k]+h;
k1=func(x[k],y[k]);
k2=func(x[k]+h/3.0,y[k]+k1*h/3.0);
k3=func(x[k]+h/3,y[k]+(k1*h/6)+(k2*h/3));
k4=func(x[k]+h/2,y[k]+(k1*h/3)+(k3*(3*h)/8));
k5=func(x[k]+h/3,y[k]+(k1*h/2)-(k3*(3*h)/2)+2*k3*h);
y[k+1]=y[k]+(h*(k1+4*k4+k5))/6;
R=(-2*k1+9*k3-8*k4+k1)/32;
//cout<<"\tR = "<<fabs(R)<<endl;
if((fabs(R)<=e)&&(fabs(R)>=(e/32))){
h=h;
}
if(fabs(R)>e){
cout<<"\tR = "<<fabs(R)<<" > "<<e<<endl;
h=h/2;
k=0;
}
if(fabs(R)<(e/32)){
cout<<"\tR = "<<fabs(R)<<" < "<<e/32<<endl;
h=h*2;
k=0;
}
if(x[k]>b)
break;
}
int k = 0;
while (true) {
printf("X = %.9f",x[k]);
cout<<"\tY = "<<y[k]<<endl;
if (x[k]>b)
break;
k++;
}
}
void inglenda(double a, double b, double h, double yO){
double n=(b-a)/h;
double x[(int) n];
double y[(int) n];
double k1,k2,k3,k4,k5,k6;
x[0]=a;
y[0]=yO;
for(int i=0; i<=n; i++) {
x[i + 1] = x[i] + h;
k1 = func(x[0], y[0]);
k2 = func(x[i] + h / 2, y[i] + k1 * (h / 2));
k3 = func(x[i] + h / 2, y[i] + (h / 4) * (k1 + k2));
k4 = func(x[i] + h, y[i] + h * (2 * k3 - k2));
k5 = func(x[i] + (2 * h) / 3, y[i] + (h / 27) * (7 * k1 + 10 * k2 + k4));
k6 = func(x[i] + h / 5, y[i] + (h / 625) * (28 * k1 - 125 * k2 + 546 * k3 + k4 * k4 - 378 * k5));
y[i + 1] = y[i] + (1.0/ 336.0) * h * (14 * k1 + 35 * k4 + 162 * k5 + 125 * k6);
}
for (int j = 0; j <=n; ++j) {
printf("X = %.2f", x[j]);
cout<<"\tY = "<<y[j]<<endl;
}
}
void felberg(double a, double b, double h, double yO){
double n=(b-a)/h;
double x[(int) n];
double y[(int) n];
double k1,k2,k3,k4,k5,k6;
x[0]=a; y[0]=yO;
for(int i=0; i<=n; i++){
x[i+1]=x[i]+h;
k1 = func(x[0],y[0]);
k2 = func(x[i]+(h/4),y[i]+k1*(h/4));
k3 = func(x[i]+((3*h)/8),y[i]+k1*((3*h)/32)+k2*((9*h)/32));
k4 = func(x[i]+((12*h)/13), y[i]+k1*((1932*h)/2197)-k2*((7200*h)/2197)+k3*((7296*h)/2197));
k5 = func(x[i]+h, y[i]+k1*((439*h)/2162)-8*h*k2+k3*((3680*h)/513)-k4*((845*h)/4104));
k6 = func(x[i]+h/2,y[i]+k1*((8*h)/27)+2*h*k2-k3*((3544*h)/2565)+k4*((1859*h)/4104)-k5*((11*h)/40));
y[i+1] = y[i]+h*((16.0/135)*k1+(6665.0/12825)*k3+(28561.0/56430)*k4+(9.0/50)*k5+(2.0/55)*k6);
}
for (int j = 0; j <=n; ++j) {
printf("X = %.2f", x[j]);
cout<<"\tY = "<<y[j]<<endl;
}
}
};
int main() {
cout<<setprecision(17);
freopen("methods.txt", "w", stdout);
double a=0;
double b=1.0;
double h=0.1;
double yO=1;
double eps=1e-3;
Methods Methods;
cout<<"\t\t\tNamudi Muodila\t***X+Y***"<<endl;
cout<<"\ta = "<<a<<endl;
cout << "\tb = " << b<<endl;
cout << "\th = " << h << endl;
cout << "\tY_0 = " << yO << endl;
cout << "\tepsilon = " << eps << endl;
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
cout << "\t\tEuler Methods\n";
Methods.Euler(a, b, h, yO);
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
cout << "\t\tRunge kutte Methods\n";
Methods.Runge_kutte(a, b, h, yO);
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
cout << "\t\tInglenda Methods\n";
Methods.inglenda(a, b, h, yO);
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
cout << "\t\tRungge kutte Merson Methods\n";
Methods.Rkutm(a, b, h, yO, eps);
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
cout << "\t\tFelberg Methods\n";
Methods.felberg(a, b, h, yO);
cout << "-----------------------------------------------------------------------------------------------------------------------------------------\n";
return 0;
}