Question

Using MATLAB Solve x - 2t = 0, (0)0,(0) = 0.1, [0, 3] by any convenient method. Graph the solution on

Use fourth-order Runge-Kutta method

Answer 1

chane Oint Sine u '- u' =) * Sin trava sysdem o ode FaiYh oxdey du t dt hgltn, un,Un) k2h tltnt unt k3-h(unt,) unt 2+ 4 ) un, Un) , gltn, un,Un--u,it and Scanned with CamScanner

%%%%%%%%%%%%%MATLAB Code

clc;
clear all;
format long

f=@(t,u,v)v; % function 1
g=@(t,u,v)-v-u^2+2*t; % function 2

h=0.01; % step size
a=0; % initila point
b=3; % final point

  
t=a:h:b;
n=(b-a)/h; % number of points
% Initial conditons
u(1)=0;
v(1)=0.1;

%Rk4 for system
for i=1:n
K1=h*f(t(i),u(i),v(i));
L1=h*g(t(i),u(i),v(i));

  
K2=h*f(t(i)+h/2,u(i)+K1/2,v(i)+L1/2);
L2=h*g(t(i)+h/2,u(i)+K1/2,v(i)+L1/2);

  
K3=h*f(t(i)+h/2,u(i)+K2/2,v(i)+L2/2);
L3=h*g(t(i)+h/2,u(i)+K2/2,v(i)+L2/2);

  
K4=h*f(t(i)+h,u(i)+K3,v(i)+L3);
L4=h*g(t(i)+h,u(i)+K3,v(i)+L3);
  
u(i+1)=u(i)+(1/6)*(K1+2*K2+2*K3+K4);
v(i+1)=v(i)+(1/6)*(L1+2*L2+2*L3+L4);

end
plot(t,u,'linewidth',2)

xlabel('t')
ylabel('u')

3 2,5 3 1.5 1 0.5 0 0 2,5 3 2 1.5 1 0.5 t