graphing my first PDE

Hello! I am new to Matlab and trying to graph my first PDE. I have no idea how it works, can any one help me with how to write the script for the following PDE

c(∂u∂x) + ∂u∂t = 0 with initial condition u(x, 0) = arctan(x). Plot the solution to this PDE for a few different values of c (small, large, positive, negative)

Thanks :)

Answer 1

[Rushan]

how do find the correct boundary conditions when (initial condition) uo = atan(x) and the PDE equation is c(∂u∂x) + ∂u∂t = 0 ?

Answer 2

[David Sanchez]

take a look at the documentation.

doc pdepe

will present a very good example. This same example is explained in more detail in the following link:

http://man.fsid.cvut.cz/matlab6_r13/techdoc/math_anal/diffe29a.html

You can easily adapt that example to solve your problem

[Rushan]

thanks for the link. I tried writing the script for the equation, but i'm getting an error :(

PDE equation: c(∂u∂x) + ∂u∂t = 0

PDE equation in MATLAB format: 1/-c (DuDt) = x^-0 (x^0 DuDx) + 0 (not sure if its correct)

Here is my script: ---------------------------------------------------------------------------

function [c,f,s] = pdex1pde(x,t,u,DuDx)

c = -1;

f = DuDx;

s = 0;

function u0 = pdex1ic(x)

u0 = arctan(x);

function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)

pl = ul;

ql = 0;

pr = 5;

qr = 1;

m = 0;

x = linspace(0,1,20);

t = linspace(0,2,5);

sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);

u = sol(:,:,1);

surf(x,t,u)

title('Numerical solution computed with 20 mesh points')

xlabel('Distance x')

ylabel('Time t')

---------------------------------------------------------------------------

Please Help me out !!! :(