MATLAB: Finite difference method problem with solving an equation

finite difference method

Trying to use Finite difference method, to write the equation in AT = b matrices. But I don't know how to write FDM on that type of equation, please see image.

Best Answer

(k(x_(i+1/2))*(T(x_(i+1))-T(x_(i)))/(x_(i+1)-x_(i))-k(x_(i-1/2))*(T(x_(i))-T(x_(i-1)))/(x_(i)-x_(i-1)))/(x_(i+1/2)-x_(i-1/2)) = Q(x_i)

with

x_(i+1/2)=(x_(i+1)+x_(i))/2
x_(i-1/2)=(x_(i)+x_(i-1))/2

Best wishes

Torsten.

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MATLAB: Solve a system of ODE

 function [t,x]=euleroesplicito(fcn,t0,x0,h,tend)
    n = fix((tend-t0)/h)+1; 
    t = linspace(t0,t0+(n-1)*h,n); 
    x = zeros(n,length(x0)); 
    x(1,:) = x0; 
    for i = 2:n 
        x(i,:) = x(i-1,:) + h*feval(fcn,t(i-1),x(i-1,:))'; 
    end
end

Note that I have reversed the sequence of outputs to make it conform to Matlab's ODE standard. Test on the equatiion for free fall:

 g = -9.81;
 [t,x] = euleroesplicito(@(t,x) [x(2);g],0,[10;0],0.01,1);
 plot(t,x(:,1));

MATLAB: Help with Understanding and Fixing Contour Plot

I am not certain what you’re doing, or the result you want.

This sets the elements of ‘T2d’ that are equal to 1, to NaN, since NaN values do not plot, and that appears to be outside the area you want to plot.

See if that change, and figure(2) (the surf plot, rotated to match your ‘T2d’ matrix) do what you want. These lines replace your code after the ‘X’ and ‘Y’ assignments:

T2d(T2d == 1) = NaN;
figure(1)
contourf(x,y,T2d,10)
figure(2)
surf(T2d)
grid on
view(0, -90)
shading interp

Best Answer

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MATLAB: Solve a system of ODE

MATLAB: Help with Understanding and Fixing Contour Plot

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