MATLAB: Solve two ODE with IVP euler

eulerivpMATLABmatlab functionodeplot

I know how to solve a simple ode using euler but confused with putting initial values and solving them

if I have two ODE

dx1/dt=x1*t+x2

and

dx2/dt=2*x1-x2*t

now I have been given initial values/guess

x1,0=1

x2,0=2

delta(t)=0.0001h

and I need to evaluate this ODE using IVP euler from t=0 to t=1h

Best Answer

Hi @shubham kumar gupta

This is one of several ways to simulate the time-varying dynamics.

tspan  = 0:0.0001:1;	% simulation time and step size
y0 = [1; 2];			% initial condition
[t, y] = ode45(@(t,y) [t*y(1) + y(2); 2*y(1) - t*y(2)], tspan, y0);
plot(t, y)

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

Here's a version:

% Initial conditions
t0=0;
x0=0:0.2:1;
y0=1:0.2:2;
dt=0.1;
tz=1;
t_range= t0:dt:tz;
X = zeros(numel(x0),numel(t_range));
Y = zeros(numel(y0),numel(t_range));
x_rk=zeros(1,numel(t_range));
y_rk= zeros(1,numel(t_range));
for n = 1:numel(x0)
    x_rk(1)=x0(n);
    y_rk(1)=y0(n);
    for i=1:length(t_range)-1
        [x_rk(i+1), y_rk(i+1)]=rk_method(x_rk(i),y_rk(i),dt);
    end
    X(n,:) = x_rk;
    Y(n,:) = y_rk;
    %% PLots
    subplot(numel(x0)/2,2,n)
    plot (t_range, x_rk,'b-o',t_range, y_rk,'y-o','MarkerSize',5);
    grid
    title([num2str(x0(n)),'   ',num2str(y0(n))])
    legend('x','y')
end
disp('X = '), disp(X)
disp('Y = '), disp(Y)
%% Functions
function [dxdt, dydt]= f(x,y)
dxdt =  5*x-3*y;
dydt = -6*x+2*y;
end 
function [x1, y1]=rk_method(x0,y0,dt)
[k11, k12]=f(x0,y0);     
[k21, k22]=f(x0+0.5*dt*k11,y0+0.5*dt*k12); 
[k31, k32]=f(x0+0.5*dt*k21,y0+0.5*dt*k22); 
[k41, k42]=f(x0+dt*k31, y0+dt*k32); 
x1=x0+dt*((k11/6)+((k21+k31)/3)+(k41/6));
y1=y0+dt*((k12/6)+((k22+k32)/3)+(k42/6));
end

MATLAB: Solving a ODE in matlab

ode = @(t,y) y.^2-y.*0.1*cos(2.*t)-0.2*cos(2.*t);
t=[0 8];
y0 = -1;
[t,y] = ode45(ode,t,y0);
plot(t,y)

Best Answer

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

MATLAB: Solving a ODE in matlab

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