MATLAB: Solve second order non-linear partial differential equation with boundaries conditions

differentiation partial differential equation boundaries conditions

hello everyone!

I am struggling to find a way to solve this equation

with those boundaries condition

where a, b, pac, pev are known constants

hope someone can help me,

thank you!

Best Answer

Hi Alessia,

There are many way to solve the above differential equation and some of them are well documented, refer to bvp4c function, it is really good way of solving boundary condition differential equation(@darova also recommend this function in the comments section). There are other ways to solve this, check out this example link.

I hope this references helps you.

Cheers.

Related Solutions

MATLAB: Initial guess for bvp4c

There are three parts to this problem:

1. Error: Too many input arguments.

To solve this issue, the second argument to bvpinit should have 2 entries instead of 3. This is an initial guess for all the mesh points. The fsode function accepts the y input argument which is expected to be a 2-length vector in your case. You can read more about 'yinit' argument here: https://www.mathworks.com/help/matlab/ref/bvpinit.html#mw_1c665a1d-6f2b-438a-95eb-6c6a2cd19026

solinit = bvpinit(linspace(0,infinity,2),[25 0]);

2. Even with this change you will see an error that the defined constants are not available inside the functions.

To do that, you will have to pass them as inputs to your fsode and fsbc functions. Some examples are available here: https://www.mathworks.com/matlabcentral/answers/274406-ode45-extra-parameters#comment_351560. Some sample code is given below which you can adapt from:

sol = bvp4c(@(x,y) fsode(x,y,rsco,rje,rd,beta_,pac,pev,fi_), ...
    @(y0,y1) fsbc(y0,y1,rsco,rje,rd,beta_,pac,pev,fi_),...
    solinit);
function dfdeta = fsode(x,y,rsco,rje,rd,beta_,pac,pev,fi_) %Function 
 dfdeta = [y(2)
        (4/beta_)*((y(1))^(1/4)-1)];
end
function res = fsbc(y0,y1,rsco,rje,rd,beta_,pac,pev,fi_) %Boundaries Conditions
res = [y0(1)
      -((4*fi_)/beta_)*(y1(1)^(1/4)-1+pac-pev)];
end

3. With these changes, the script would compile but might throw warnings.

If you see the warning: Unable to meet the tolerance without using more than 5000 mesh points...

You could experiment with appropriate initial choices and boundary conditions. You can also refer to the answer here for some ideas.

Here are a couple of examples from the Docs which should help you better understand how the bvp4c and the bvpinit functions can be used:

a. Solve Second-Order BVP

b. Using bvpinit for an initial guess of BVP solution

MATLAB: How to use bvp4c for boundary value problem with 2 unknown parameters

fprintf('For r=%4.2f a= %4.2f \n',sol.parameters);

Best wishes

Torsten.

Best Answer

Related Solutions

MATLAB: Initial guess for bvp4c

MATLAB: How to use bvp4c for boundary value problem with 2 unknown parameters

Related Question