MATLAB: How can I write a simple pde and solve it

pde

I want to write pde in matlab , how can i do it ,

for ex I want to wite this equation :

(∂^2 f(x,y))/(∂x^2 )+(∂^2 f(x,y))/(∂y^2 )=0

I tried the following code in the command window :

>> syms f(x,y)
>> diff( f(x,y) ,x ,x) + diff( f(x,y) ,y ,y)== 0

Is it right ??

then how can I find the solution?

Or what is the right way to write this eq and solve it?

Best Answer

Unfortunately MATLAB does not have any symbolic pde tools.

According to Maple, the solution is

(y^2-x^2) * C2/2 + C1*x + C3*y + f00

where f00 is f(0,0), and where C1 and C3 are constants of integration that will vary according to the boundary conditions, and where C2 is an arbitrary constant

Related Solutions

MATLAB: Differential equation with mixed linear and log derivatives – proper setting

Using chain-rule, we can write

Therefore, the equation can be written as

syms y(x) f
eq = diff(log(y),x)*1/diff(log(x),x) + diff(log(diff(y,x)),x)*1/diff(log(x),x) + ...
    diff(y,x)*1/diff(log(x),x)*log(x) + y ...
    == 1 + f;
sol = dsolve(eq);

The symbolic solution is

>> sol
sol =
  ((2*C2*x^y + C2*f*x^y - C2*x^y*y + 2*C1*x^f*x^2)/(x^y*(f - y + 2)))^(1/2)
 -((2*C2*x^y + C2*f*x^y - C2*x^y*y + 2*C1*x^f*x^2)/(x^y*(f - y + 2)))^(1/2)

For numerical solution, try this

syms y(x) f
eq = diff(log(y),x)*1/diff(log(x),x) + diff(log(diff(y,x)),x)*1/diff(log(x),x) + ...
    diff(y,x)*1/diff(log(x),x)*log(x) + y ...
    == 1 + f;
eq2 = odeToVectorField(eq);
odeFun = matlabFunction(eq2, 'Vars', {'x', 'Y', 'f'});
xspan = [0.1 10];
xs = 0.1:0.001:10;
fv = rand(size(xs));
ffun = @(x) interp1(xs, fv, x);
ic = [1; 2];
[t, y] = ode45(@(x, y) odeFun(x, y, ffun(x)), xspan, ic);
plot(t, y);

MATLAB: Basic questions how to find x

y=@(x) 5*x+2 
y(2)

Best Answer

Related Solutions

MATLAB: Differential equation with mixed linear and log derivatives – proper setting

MATLAB: Basic questions how to find x

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