Plotting the exact and numerical solutions on the same plot

Question

Bas123 2023-5-1

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1955664-plotting-the-exact-and-numerical-solutions-on-the-same-plot

评论： Bas123 2023-5-1

I am working on a numerical analysis problem where I need to draw the exact and numerical solutions on the same figure. The numerical method used is the Runge-Kutta method of order 4. Here is my code.

function [t, x] = RK4Method(f, x_0, t_initial, t_m, n)
%time step
h = (t_m - t_initial) / n;
%arrays for t and x
t = linspace(t_initial, t_m, n+1);
x = zeros(1, n+1);
x(1) = x_0;
%RK4 iterations
for i = 1:n
    k1 = h * f(t(i), x(i));
    k2 = h * f(t(i) + h/2, x(i) + k1/2);
    k3 = h * f(t(i) + h/2, x(i) + k2/2);
    k4 = h * f(t(i) + h, x(i) + k3);
    x(i+1) = x(i) + 1/6 * (k1 + 2*k2 + 2*k3 + k4);
end

Here is the command that I used to draw the numerical solution.

f = @(t, x) (x-t^2+1);
[t, x] = RK4Method(f, 0.5, 0, 2, 200);
plot(t, x);
xlabel('time');
ylabel('x');

The code used to draw the exact solution is given below.

fplot(@(t) (t^2+2*t+1-(1/2)*e^t, [0 2])

Could someone please help me with drawing the two solutions on the same plot? Thank you!

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Answer 1

Simon Chan 2023-5-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1955664-plotting-the-exact-and-numerical-solutions-on-the-same-plot#answer_1226424

在 MATLAB Online 中打开

Just add hold on

f = @(t, x) (x-t^2+1);
[t, x] = RK4Method(f, 0.5, 0, 2, 200);
plot(t, x);
xlabel('time');
ylabel('x');
hold on;                                                                % Add this
fplot(@(t) t.^2+2*t+1-(1/2)*exp(t), [0 2],'r--','LineWidth',4);         % <--- Modify this     