- Use mesh/meshgrid to define the u function in x and t.
- Re-map t: t=linspace(0,1,101), then t(30)=0.3
Solving a wave equation in matlab
56 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Here is the problem statement:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283202/image.png)
I am having trouble plotting the solution at t=0.3 and not sure if my code is solving the wave equation correctly. This is what I have, but not sure where to go from here. Any help would be great thanks!
xstep = 0.1;
tstep = 0.05;
xstep2 = xstep*xstep;
tstep2 = tstep*tstep;
alpha = 2;
alpha2 = alpha*alpha;
lambda2 = alpha2*tstep2/xstep2;
xdomain = [0 1];
tdomain = [0 1];
nx = round((xdomain(2)-xdomain(1))/xstep);
nt = round((tdomain(2)-tdomain(1))/tstep);
xt0 = zeros((nx+1),1); % initial condition
dxdt0 = zeros((nx+1),1); % initial derivative
xold = zeros((nx+1),1); % solution at timestep k
x2old = zeros((nx+1),1); % solution at timestep k-1
xnew = zeros((nx+1),1); % solution at timestep k+1
% initial condition
pi = acos(-1.0);
for i=1:nx+1
xi = (i-1)*xstep;
if(xi>=0 && xi<=1)
xt0(i) = sin(2*pi*xi);
dxdt0(i) = alpha*pi*sin(2*pi*xi);
xold(i) = xt0(i)+dxdt0(i)*tstep;
xold(i) = xold(i) - 4*pi*pi*sin(2*pi*xi)*tstep2*alpha2;
end
end
close all
syms x
t=0.3;
x=linspace(xdomain(1),xdomain(2),nx+1);
analy= sin(2*pi*x)*(sin(4*pi*t)+cos(4*pi*t));
h1=plot(x,analy,'linewidth',2);
hold on;
h2=plot(x,xold(:,t),'linewidth',2);
hold on;
h3=plot(x,xnew(:,t),'linewidth',2);
hold off
legend('Analytical','Initial','Final')
xlabel('x [m]');
ylabel('Displacement [m]');
set(gca,'FontSize',16);
for k=2:nt
time = i*tstep;
for i=1:nx+1
% Use periodic boundary condition, u(nx+1)=u(1)
if(i==1)
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(i+1)+xold(nx+1)) - x2old(i);
elseif(i==nx+1)
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(1)+xold(i-1)) - x2old(i);
else
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(i+1)+xold(i-1)) - x2old(i);
end
end
x2old=xold;
xold = xnew;
if(mod(k,2)==0)
h3.YData = xnew;
refreshdata(h3);
pause(0.5);
end
end
1 Kommentar
Optics Wizard
am 9 Apr. 2020
I haven't gone through your code on the full-scale, but your time-mapping is currently incorrect. You can only index values by integers, but you're currently indexing to data point 0.3:
h2=plot(x,xold(:,t),'linewidth',2);
For instance, when t=0.3, this line returns an error.
Some options:
I hope that helps!
Antworten (1)
Sulaymon Eshkabilov
am 30 Okt. 2021
Here is a part of your code that is corrected:
xstep = 0.1;
tstep = 0.05;
xstep2 = xstep*xstep;
tstep2 = tstep*tstep;
alpha = 2;
alpha2 = alpha*alpha;
lambda2 = alpha2*tstep2/xstep2;
xdomain = [0 1];
tdomain = [0 1];
nx = round((xdomain(2)-xdomain(1))/xstep);
nt = round((tdomain(2)-tdomain(1))/tstep);
xt0 = zeros((nx+1),1); % initial condition
dxdt0 = zeros((nx+1),1); % initial derivative
xold = zeros((nx+1),1); % solution at timestep k
x2old = zeros((nx+1),1); % solution at timestep k-1
xnew = zeros((nx+1),1); % solution at timestep k+1
% initial condition
pi = acos(-1.0);
for i=1:nx+1
xi = (i-1)*xstep;
if(xi>=0 && xi<=1)
xt0(i) = sin(2*pi*xi);
dxdt0(i) = alpha*pi*sin(2*pi*xi);
xold(i) = xt0(i)+dxdt0(i)*tstep;
xold(i) = xold(i) - 4*pi*pi*sin(2*pi*xi)*tstep2*alpha2;
end
end
close all
syms x
t=0.3;
x=linspace(xdomain(1),xdomain(2),nx+1);
analy= sin(2*pi*x)*(sin(4*pi*t)+cos(4*pi*t));
h1=plot(x,analy,'linewidth',2);
hold on;
h2=plot(x,xold(:,end),'linewidth',2); % Index issue in xold
hold on;
h3=plot(x,xnew(:,end),'linewidth',2); % Index issue in xnew
hold off
legend('Analytical','Initial','Final')
xlabel('x [m]');
ylabel('Displacement [m]');
set(gca,'FontSize',16);
for k=2:nt
time = i*tstep;
for i=1:nx+1
% Use periodic boundary condition, u(nx+1)=u(1)
if(i==1)
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(i+1)+xold(nx+1)) - x2old(i);
elseif(i==nx+1)
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(1)+xold(i-1)) - x2old(i);
else
xnew(i) = 2*(1-lambda2)*xold(i) + lambda2*(xold(i+1)+xold(i-1)) - x2old(i);
end
end
x2old=xold;
xold = xnew;
if(mod(k,2)==0)
h3.YData = xnew;
refreshdata(h3);
pause(0.5);
end
end
2 Kommentare
Siehe auch
Kategorien
Mehr zu Eigenvalue Problems finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!