# Can this be arranged to run

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MINATI on 26 Sep 2020
Commented: MINATI on 26 Sep 2020
function [u,x,y] = poisson(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter)
x0 = D(1); xf = D(2); y0 = D(3); yf = D(4);
dx = (xf - x0)/Mx; x = x0 + [0:Mx]*dx;
dy = (yf - y0)/My; y = y0 + [0:My]'*dy;
Mx1 = Mx + 1; My1 = My + 1;
%Boundary conditions
for m = 1:My1, u(m,[1 Mx1])=[bx0(y(m)) bxf(y(m))]; end %left/right side
for n = 1:Mx1, u([1 My1],n) = [by0(x(n)); byf(x(n))]; end %bottom/top
%initialize as the average of boundary values
sum_of_bv = sum(sum([u(2:My,[1 Mx1]) u([1 My1],2:Mx)']));
u(2:My,2:Mx) = sum_of_bv/(2*(Mx + My - 2));
for i = 1:My
for j = 1:Mx
F(i,j) = f(x(j),y(i)); G(i,j) = g(x(j),y(i));
end
end
dx2 = dx*dx; dy2 = dy*dy; dxy2 = 2*(dx2 + dy2);
rx = dx2/dxy2; ry = dy2/dxy2; rxy = rx*dy2;
for itr = 1:MaxIter
for j = 2:Mx
for i = 2:My
u(i,j) = ry*(u(i,j + 1)+u(i,j - 1)) + rx*(u(i + 1,j)+u(i - 1,j)) + rxy*(G(i,j)*u(i,j)- F(i,j));
end
end
if itr > 1 & max(max(abs(u - u0))) < tol, break; end
u0 = u;
end
%solve_poisson
f = inline('0','x','y'); g = inline( '0','x','y');
x0 = 0; xf = 4; Mx = 20; y0 = 0; yf = 4; My = 20;
bx0 = inline( 'exp(y) - cos(y)','y'); bxf = inline( 'exp(y)*cos(4) - exp(4)*cos(y)','y');
by0 = inline( 'cos(x) - exp(x)','x'); byf = inline( 'exp(4)*cos(x) - exp(x)*cos(4)','x');
D = [x0 xf y0 yf]; MaxIter = 500; tol = 1e-4;
[U,x,y] = poisson(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter);
clf, mesh(x,y,U), axis([0 4 0 4 -100 100])
Rik on 26 Sep 2020
The default of the run button is to run a function without any inputs. So you defined some variables, but you didn't actually provided any inputs to your function.

Walter Roberson on 26 Sep 2020
In a new file, put in the code
f = @(x,y) exp(x) + sin(y);
g = @(x,y) exp(x) .* sin(y);
x0 = 0; xf = 4;
Mx = 20;
My = 20;
y0 = 0; yf = 4;
D = [x0 xf y0 yf];
bx0 = @(y) exp(y) - cos(y);
bxf = @(y) exp(y)*cos(4) - exp(4)*cos(y);
by0 = @(x) cos(x) - exp(x);
byf = @(x) exp(4)*cos(x) - exp(x)*cos(4);
MaxIter = 500;
tol = 1e-4;
[u,x,y] = poisson(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter);
Now you can use the green run button on that new file.
I notice that you are using cos() with values that can be up to 4. Are you sure you want your units to be radians, and not degrees?
MINATI on 26 Sep 2020
Dear Walter
it is ok now
Thanks
I notice that you are using cos() with values that can be up to 4. Are you sure you want your units to be radians, and not degrees?
I will modify this for my work.
Thanks Again