Ex4-Runge Kutta-to-h0.01

//solução através do RK, intervalo h=0.01

//𝑝𝑎𝑟𝑎 𝑥(0) = 0.1 𝑒 0.1 ≤ 𝑡 ≤ 1,3�

clc
clear
ya(1)=0.1;yb(1)=0.1;yc(1)=0.1;
h=0.01;
t(1)=0.1;
tfinal=1.3;
n=tfinal/h;
for k=1:n-1
 t(k+1)=t(k)+h;
 
//RUNGE KUTTA PRIMEIRA ORDEM
 ya(k+1)=ya(k)+h*((ya(k)/t(k))+t(k)*ya(k)^2);
 
//RUNGE KUTTA SEGUNDA ORDEM
yb(k+1)=yb(k)+(h/2)*((yb(k)/t(k))+(t(k)*yb(k)^2)+((yb(k)+h*((yb(k)/t(k))+(t(k)*yb(k)^2)))/(t(k+1)))+(t(k+1))*(yb(k)+h*((yb(k)/t(k))+(t(k)*yb(k)^2)))^2);

//RUNGE KUTTA QUARTA ORDEM
 k1=h*((yc(k)/t(k))+(t(k)*yc(k)^2));
 k2=h*(((yc(k)+(k1/2))/(t(k)+(h/2)))+(t(k)+(h/2))*(yc(k)+(k1/2))^2);
 k3=h*(((yc(k)+(k2/2))/(t(k)+(h/2)))+(t(k)+(h/2))*(yc(k)+(k2/2))^2);
 k4=h*(((yc(k)+k3)/(t(k)+h))+(t(k)+h)*(yc(k)+k3)^2);
 yc(k+1)=yc(k)+1/6*(k1+2*k2+2*k3+k4);
 
end
figure(1)
plot(t,ya,'r',t,yb,'b',t,yc,'g');
legend('RK 1','RK 2','RK 4');
title('Exercício 4 - h=0.01')
xlabel('t (s)')
ylabel('y')