How to make graph that plot between Analytical Solution (Exact Solution) and Numerical Method Solution?

7 次查看（过去 30 天）
Yusuf Arya Yudanto
评论： Yusuf Arya Yudanto 2022-3-6
Greetings!
Can someone help to guide me how to make graph that plot between Analytical Solution (Exact Solution) and Adams-Moulton Solution? Here I attached my script.
%% 2nd-order Adams-Moulton Solution
fun = @(t,y) ((1+4*t)*((y)^1/2));
y0 = 1;
tspan = [0,1];
N = 4;
%% Initial Values
h = (tspan(2) - tspan(1))/N;
exactY = @(t) (((3*t)/2)+3*t.^2).^(2/3);
t1 = tspan(1) + h; y1 = exactY(t1);
t2 = tspan(1) + 2*h; y2 = exactY(t2);
[t2,Y2] = AM2(fun,tspan,y0,y1,N);
%% Display Solution
Y = exactY(t2);
disp('-----------------------------');
disp('t_i y(t_i) AM2 Error')
disp('-----------------------------');
formatSpec = '%.2f %.5f %.5f %.5f\n';
fprintf(formatSpec,[t2';Y';Y2';abs(Y'-Y2')])
I really appreciate any help you can provide. Thank you.
  4 个评论
显示 2更早的评论
Torsten
Torsten 2022-3-5
fun = @(t,y) (1+4*t)*sqrt(y);
y0 = 1;
tspan = [0,1];
N = 4;
%% Initial Values
h = (tspan(2) - tspan(1))/N;
exactY = @(t)(t/2 + t.^2 + 1).^2;
t1 = tspan(1) + h; y1 = exactY(t1);
[T,Ynum] = AM2(fun,tspan,y0,y1,N);
%% Display Solution
Yexact = exactY(T);
plot(T,[Ynum,Yexact])
function [t,y] = AM2(fun,tspan,y0,y1,N)
a = tspan(1);
b = tspan(2);
h = (b-a)/N;
t = zeros(N+1,1);
y = zeros(N+1,1);
t(1) = a; y(1) = y0;
t(2) = a+h; y(2) = y1;
for i = 2:N
t(i+1) = t(i) + h;
Fi = fun(t(i),y(i));
Fi1 = fun(t(i-1),y(i-1));
funh = @(yh) yh - y(i) - h/12*(5*fun(t(i+1),yh) + 8*Fi - Fi1);
y(i+1) = fsolve(funh,y(i));
end
end

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Alan Stevens
Alan Stevens 2022-3-5
After Y = exactY(t2) you probably need something like:
plot(t2,Y2,t2,Y)
legend('AM','Exact')
However, you haven't supplied the code for your AM function, so I can't check!
  6 个评论
显示 4更早的评论

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 MATLAB 的更多信息

标签

产品


版本

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by