Matlab to solve finite difference for Ode

% Finite difference method

% Approximate the solution of y"=(-2/x)y'+(2/x^2)y+ sin(lnx)/x^2

% for 1<=x<=2 with y(1)=1 and y(2)=2.

p = @(x) (-2/x);

q = @(x) (2/x^2);

r = @(x) (sin(log(x))/x^2);

aa = 1; bb = 2; alpha = 1; beta = 2; n=29;      % h = (bb-aa)/(n+1);   h=0.1

fprintf('   x           w   \n');

h = (bb-aa)/(n+1);

a = zeros(1,n+1);

b = zeros(1,n+1);

c = zeros(1,n+1);

d = zeros(1,n+1);

l = zeros(1,n+1);

u = zeros(1,n+1);

z = zeros(1,n+1);

w = zeros(1,n+1);

x = aa+h;

a(1) = 2+h^2*q(x);

b(1) = -1+0.5*h*p(x);

d(1) = -h^2*r(x)+(1+0.5*h*p(x))*alpha;

m = n-1;

for i = 2 : m

x = aa+i*h;

a(i) = 2+h^2*q(x);

b(i) = -1+0.5*h*p(x);

c(i) = -1-0.5*h*p(x);

d(i) = -h^2*r(x);

end

x = bb-h;

a(n) = 2+h^2*q(x);

c(n) = -1-0.5*h*p(x);

d(n) = -h^2*r(x)+(1-0.5*h*p(x))*beta;

l(1) = a(1);

u(1) = b(1)/a(1);

z(1) = d(1)/l(1);

for i = 2 : m

l(i) = a(i)-c(i)*u(i-1);

u(i) = b(i)/l(i);

z(i) = (d(i)-c(i)*z(i-1))/l(i);

end

l(n) = a(n)-c(n)*u(n-1);

z(n) = (d(n)-c(n)*z(n-1))/l(n);

w(n) = z(n);

for j = 1 : m

i = n-j;

w(i) = z(i)-u(i)*w(i+1);

end

i = 0;

fprintf('%5.4f    %11.8f\n', aa, alpha);

for i = 1 : n

x = aa+i*h;

fprintf('%5.4f    %11.8f\n', x, w(i));

end

i = n+1;

fprintf('%5.4f    %11.8f\n', bb, beta);am trying to run d code but it keeps writing Error: Invalid text character. The text ' ' contains an unsupported non-ASCII whitespace character. Please where am I doing wrong?

Answer 1

[Viranch Patel]

I tried running the code on my machine and it's working fine. You can paste this code to your machine and see if its working. I am attaching the output too. You might be using some wrong character for any particular character which is not supported.

% Finite difference method
% Approximate the solution of y"=(-2/x)y'+(2/x^2)y+ sin(lnx)/x^2
% for 1<=x<=2 with y(1)=1 and y(2)=2.
p = @(x) (-2/x);
q = @(x) (2/x^2);
r = @(x) (sin(log(x))/x^2);
aa = 1; bb = 2; alpha = 1; beta = 2; n=29;      % h = (bb-aa)/(n+1);   h=0.1
fprintf('   x           w   \n');
h = (bb-aa)/(n+1);
a = zeros(1,n+1);
b = zeros(1,n+1);
c = zeros(1,n+1);
d = zeros(1,n+1);
l = zeros(1,n+1);
u = zeros(1,n+1);
z = zeros(1,n+1);
w = zeros(1,n+1);
x = aa+h;
a(1) = 2+h^2*q(x);
b(1) = -1+0.5*h*p(x);
d(1) = -h^2*r(x)+(1+0.5*h*p(x))*alpha;
m = n-1;
for i = 2 : m
    x = aa+i*h;
    a(i) = 2+h^2*q(x);
    b(i) = -1+0.5*h*p(x);
    c(i) = -1-0.5*h*p(x);
    d(i) = -h^2*r(x);
end
x = bb-h;
a(n) = 2+h^2*q(x);
c(n) = -1-0.5*h*p(x);
d(n) = -h^2*r(x)+(1-0.5*h*p(x))*beta;
l(1) = a(1);
u(1) = b(1)/a(1);
z(1) = d(1)/l(1);
for i = 2 : m
    l(i) = a(i)-c(i)*u(i-1);
    u(i) = b(i)/l(i);
    z(i) = (d(i)-c(i)*z(i-1))/l(i);
end
l(n) = a(n)-c(n)*u(n-1);
z(n) = (d(n)-c(n)*z(n-1))/l(n);
w(n) = z(n);
for j = 1 : m
    i = n-j;
    w(i) = z(i)-u(i)*w(i+1);
end
i = 0;
fprintf('%5.4f    %11.8f\n', aa, alpha);
for i = 1 : n
    x = aa+i*h;
    fprintf('%5.4f    %11.8f\n', x, w(i));
end
i = n+1;
fprintf('%5.4f    %11.8f\n', bb, beta);

Output:

   x           w   
1.0000     1.00000000
1.0333     1.03067949
1.0667     1.06155254
1.1000     1.09262608
1.1333     1.12390423
1.1667     1.15538887
1.2000     1.18708018
1.2333     1.21897697
1.2667     1.25107701
1.3000     1.28337728
1.3333     1.31587416
1.3667     1.34856355
1.4000     1.38144105
1.4333     1.41450201
1.4667     1.44774163
1.5000     1.48115505
1.5333     1.51473732
1.5667     1.54848354
1.6000     1.58238883
1.6333     1.61644834
1.6667     1.65065735
1.7000     1.68501118
1.7333     1.71950528
1.7667     1.75413522
1.8000     1.78889666
1.8333     1.82378540
1.8667     1.85879736
1.9000     1.89392857
1.9333     1.92917520
1.9667     1.96453354
2.0000     2.00000000

Answer 2

[Patrica]

It looks like the issue you’re encountering might be due to non-ASCII characters in your code. This can happen when copying code from a source that inserts special characters, such as different types of spaces or quotation marks that aren’t recognized by MATLAB.

To fix this:

1. Check for Hidden Characters: Carefully go through the code and replace any suspicious spaces or characters with standard ASCII ones. You can try pasting the code into a plain text editor (like Notepad) and then copy it back into MATLAB.
2. Ensure Proper Formatting: Double-check the quotation marks, operators, and any symbols for compatibility with MATLAB. Sometimes unseen formatting issues occur when copying code.
3. Use the Editor Diagnostics: MATLAB's editor can highlight issues with characters or spaces if you have diagnostics enabled.

If you continue having trouble, you might want to consult a MATLAB expert. I’ve used MATLAB Assignment Experts in the past, and they were very helpful. You can reach them via WhatsApp at [[phone]] or email at [e-mail]. Their site, www.matlabassignmentexperts.com, is a great resource, and they focus on helping you achieve perfect grades.

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