![Using MATLAB Solve 2x5 5х, x(0)0, a(0) 0.4, on the interval [-2,0] Use Taylor series method or Runge-Kutta method](http://img.homeworklib.com/images/038ac1f4-3255-49f5-b231-e2429d969a14.png?x-oss-process=image/resize,w_560)
Homework Answers
%Matlab code for RK4 solution
f1=@(t,x1,x2) x2;
f2=@(t,x1,x2) 2*x2-5*x1;
%all step size
h=-0.01;
%Initial conditions
x10=0; %x1(0)=0
x20=0.4; %x2(0)=0.4
%initial t
t0=0;
%t end values
tend=-2;
tn=t0:h:tend;
x1_rk(1)=x10; x2_rk(1)=x20; t_rk(1)=t0;
%Runge Kutta 4 iterations
for i=1:length(tn)-1
k0=h*f1(t_rk(i),x1_rk(i),x2_rk(i));
l0=h*f2(t_rk(i),x1_rk(i),x2_rk(i));
k1=h*f1(t_rk(i)+(1/2)*h,x1_rk(i)+(1/2)*k0,x2_rk(i)+(1/2)*l0);
l1=h*f2(t_rk(i)+(1/2)*h,x1_rk(i)+(1/2)*k0,x2_rk(i)+(1/2)*l0);
k2=h*f1(t_rk(i)+(1/2)*h,x1_rk(i)+(1/2)*k1,x2_rk(i)+(1/2)*l1);
l2=h*f2(t_rk(i)+(1/2)*h,x1_rk(i)+(1/2)*k1,x2_rk(i)+(1/2)*l1);
k3=h*f1(t_rk(i)+h,x1_rk(i)+k2,x2_rk(i)+l2);
l3=h*f2(t_rk(i)+h,x1_rk(i)+k2,x2_rk(i)+l2);
t_rk(i+1)=t0+i*h;
x1_rk(i+1)=double(x1_rk(i)+(1/6)*(k0+2*k1+2*k2+k3));
x2_rk(i+1)=double(x2_rk(i)+(1/6)*(l0+2*l1+2*l2+l3));
end
%plotting the result
figure(1)
plot(t_rk,x1_rk,'Linewidth',2)
xlabel('t')
ylabel('x(t)')
title('x(t) vs. t plot')
grid on
box on
%plotting the result
figure(2)
plot(t_rk,x2_rk,'Linewidth',2)
xlabel('t')
ylabel('dx(t)/dt')
title('dx(t)/dt vs. t plot')
grid on
box on
%%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%%%
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