Question

eview File Edit View 66 180s volw à MAE305 Project 5.pdf (1 page) Project 5 1. Solve ollowing initial value problem to obtain u(5), du dt 10t+50, u) (a) Use Euler's Method with h-0.01, 0.1,0.5 (b) Use the Classical RK4 method, with h-0.01,0.1,0s 2. Solve the following initial value problem to obtain u (5) and u(5), d2u d 10-S0, M(o) (a) Use Euler's Method with h-0.01,0.1,0.5 (b) Use RK4 method with h-0.01, 0.1,0.5

matlab code

Answer 1

du dt it; ?什 dt oo, o.ou

Cl dt 2. 2 Analtial dcq Ck "tseを .-5 t

clc;clear all;
%Euler method
t1(1)=0;
u1(1)=0;
h=[0.01,0.1,0.5];
figure
for j=1:3
for i=1:100
u1(i+1)=u1(i)+((50-10*t1(i))*h(j));
t1(i+1)=t1(i)+h(j);
end
plot(t1,u1)
hold on
end
xlabel('t')
ylabel('u')
title('Euler method')
legend('h=0.01','h=0.1','h=0.5')

%RK method
t2(1)=0;
u2(1)=0;
figure
for j=1:3
for i=1:100
k1=h(j)*(50-(10*t2(i)));
k2=h(j)*(50-(10*(t2(i)+0.5*h(j))));
k3=h(j)*(50-(10*(t2(i)+0.5*h(j))));
k4=h(j)*(50-(10*(t2(i)+h(j))));
du=(1/6)*(k1+(2*k2)+(2*k3)+k4);
u2(i+1)=u2(i)+du;
t2(i+1)=t2(i)+h(j);
end
plot(t2,u2)
hold on
end
xlabel('t')
ylabel('u')
title('RK4 method')
legend('h=0.01','h=0.1','h=0.5')

%analtical
t=0:0.01:50;
u=-5*t.^2+(50*t);
figure
plot(t,u)
xlabel('t')
ylabel('u')
title('Analtical equation')

Euler method 2000 h-0.01 h-0.1 -h=0.1 h=0.5 2000 4000 6000 8000 -10000 0 5 10 15 20 25 30 35 40 45 50

RK4 method 2000 h=0.01 h-0.1 h=0.5 2000 400 6000 8000 -10000 0 5 10 15 20 25 30 35 40 45 50

Analtical equation 2000 -2000 400 6000 8000 -10000 0 5 10 15 20 25 30 35 40 45 50