Matlab to solve finite difference for Ode

2021 7 7
2 个回答
更新时间：2024 12 1
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% 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
Invalid text character. The text '      ' contains an unsupported non-ASCII whitespace character.
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?

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回答（2 个）

Viranch Patel
Viranch Patel 2021-7-9

1 个投票

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
Walter Roberson
Walter Roberson 2024-12-1
Ran in:

0 个投票

Ran in:
S = 'aa = 1; bb = 2; alpha = 1; beta = 2; n=29;      % h = (bb-aa)/(n+1);   h=0.1'
S = 'aa = 1; bb = 2; alpha = 1; beta = 2; n=29;      % h = (bb-aa)/(n+1);   h=0.1'
idx = find(S>128)
idx = 1×8
43 44 45 46 47 48 69 70
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
S(idx)
ans = '        '
S(idx)+0
ans = 1×8
160 160 160 160 160 160 160 160
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Your code contains a number of char(160), which is the Unicode Non-Breaking Whitespace character https://www.compart.com/en/unicode/U+00A0
The first group of NBSP is after the n=29;
S(40:50)
ans = '29;      % '

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