i have written this code i want to solve this heat equation for n vary from 0 to n(any value) for each value of x at each case from t= 0 to 10

syms l t n x pi alpha ;

a=input(('please enter alpha:'));

b=input(('please enter length:'));

c=input(('please enter number:'));

T(x,t)= 200/pi * ((-1)^(n+1))/n * sin (n*pi*x/l)*exp(-((n*pi/t)^2)*t);

symsum( T(x,t), n, 1, n);

this code is not running can any body tel me the right code

Answer 1

[Matt Kindig]

Do you want to evaluate this numerically? Such that you have a value for T at each x and t. If so, your approach of using symsum is probably not the best way to go. Instead, I would do something like this:

a = input('please enter alpha:');  %note that this value isn't used anywhere
L = input('please enter length:');
N = input('please enter number:');
x = linspace(0, L, 50);  %for example, 50 steps
t = linspace(0, 10, 50);
[X,T] = meshgrid(x,t);   %make a big matrix
T = @(n) (200/pi).*(((-1).^(n+1))./n).*sin(n*pi*X/L).*exp(-((n*pi./T).^2).*T);   %define T(x,t,n) function

%now you can find T at n=5, for example, using
T(5)