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#include<iostream>
#include<iomanip>
#include<cmath>
using namespace std;
double func(double t)
{
double a=4*(exp(0.8*t)-exp(-0.5*t))/1.3 + 2*exp(-0.5*t);
return a;
}
double f(double t, double y)
{
y=4*(exp(0.8*t)-exp(-0.5*t))/1.3 + 2*exp(-0.5*t);
double a=4*exp(0.8*t)-(0.5*y);
return a;
}
int main()
{
double t0=0;
double y0=2;
double y;
double sum11=0;
double sum12=0;
double sum13=0;
double sum21=0;
double sum22=0;
double sum23=0;
double sum31=0;
double sum32=0;
double sum33=0;
double K1, K2, K3, K4;
double h;
//The Euler method for h=0.1
while(t0<=9.9)
{
h=0.1;
y= y0 + (h*f(t0,y0));
y0=y;
t0=t0+h;
sum11=sum11+abs(func(t0)-y);
}
//The Euler method for h=0.05
while(t0<=9.9)
{
h=0.05;
y= y0 + (h*f(t0,y0));
y0=y;
t0=t0+h;
sum12=sum12+abs(func(t0)-y);
}
//The Euler method for h=0.025
while(t0<=9.9)
{
h=0.025;
y= y0 + (h*f(t0,y0));
y0=y;
t0=t0+h;
sum13=sum13+abs(func(t0)-y);
}
//Heun's method for h=0.1
while(t0<=9.9)
{
h=0.1;
K1=f(t0,y0);
K2=f(t0+h, y0+h*K1);
y = y0+ (h*(K1+K2))/2;
y0=y;
t0=t0+h;
sum21=sum21+abs(func(t0)-y);
}
//Heun's method for h=0.05
while(t0<=9.9)
{
h=0.05;
K1=f(t0,y0);
K2=f(t0+h, y0+h*K1);
y = y0+ (h*(K1+K2))/2;
y0=y;
t0=t0+h;
sum22=sum22+abs(func(t0)-y);
}
//Heun's method for h=0.025
while(t0<=9.9)
{
h=0.025;
K1=f(t0,y0);
K2=f(t0+h, y0+h*K1);
y = y0+ (h*(K1+K2))/2;
y0=y;
t0=t0+h;
sum23=sum23+abs(func(t0)-y);
}
//4-stage Runge-Kutta method for h=0.1
while(t0<=9.9)
{
h=0.1;
K1= h*f(t0,y0);
K2=h*f(t0+ h/2, y0+ K1/2);
K3=h*f(t0+ h/2, y0+ K2/2);
K4=h*f(t0+h, y0+ K3);
y = y0 + (K1+ 2*K2+ 2*K3+ K4)/6;
y0=y;
t0=t0+h;
cout << "Values of t are: " << t0 << endl;
cout << "The approximate values are:" << y << endl;
cout << "The actual values are: " << func(t0) << endl;
cout << "The respective error is: " << abs(func(t0)-y)<< endl;
sum31=sum31+abs(y-func(t0));
}
cout << "The cumulative error is:" << sum31 << endl;
//4-stage Runge-Kutta method for h=0.05
while(t0<=9.9)
{
h=0.05;
K1=h*f(t0,y0);
K2=h*f(t0+ h/2, y0+ K1/2);
K3=h*f(t0+ h/2, y0+ K2/2);
K4=h*f(t0+h, y0+ K3);
y = y0 + (K1+ 2*K2+ 2*K3+ K4)/6;
y0=y;
t0=t0+h;
sum32=sum32+abs(func(t0)-y);
}
//4-stage Runge-Kutta method for h=0.025
while(t0<=9.9)
{
h=0.025;
K1=h*f(t0,y0);
K2=h*f(t0+ h/2, y0+ K1/2);
K3=h*f(t0+ h/2, y0+ K2/2);
K4=h*f(t0+h, y0+ K3);
y = y0 + (K1+ 2*K2+ 2*K3+ K4)/6;
y0=y;
sum33=sum33+abs(func(t0)-y);
}
setprecision(20);
cout << fixed;
cout << " " << "h" << " " << endl;
cout << " 0.1" << " " << " 0.05" << " " << " 0.025" << endl;
cout <<" Euler " << sum11 <<" " << sum12 << " " << sum13 << endl;
cout <<" Heun " << sum21 << " " << sum22 << " " << sum23 << endl;
cout <<"Runge Kutta " << sum31 << " " << sum32 << " " << sum33 << endl;
return 0;
}
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