PDE Toolbox Coefficient Specification

This is the problem. Since the PDE toolbox does not accept variable parameters, I first set theta1 and theta2 to be both 0.01.

I don't think there is any problem with my coefficients c and a, but there are issues with the f. In this situation, I cannot clearly tell when to use ".*". There is not much info about it when I am reading page 2-89 and 2-90 on https://www.mathworks.com/help/pdf_doc/pde/pde.pdf

It gives me this error message when I click solve:

Answer 1

[Torsten]

As I already answered, f has to be referenced as a function or a function handle in your case.

It cannot be given in the GUI - all inputs in the GUI can only be constant values.

c = 1;
a = 1;
theta1 = 0.1;
theta2 = 0.1;

specifyCoefficients(model,"m",0,"d",0,"c",c,"a",a,"f",@(location,state)fcoeffunction(location,state,theta1,theta2));

function f = fcoeffunction(location,state,theta1,theta2)
  N = 1; % Number of equations
  nr = length(location.x); % Number of columns
  f = zeros(N,nr); % Allocate f
  % Now the particular functional form of f
  f(1,:) = 100*sin(2*pi*location.x).*sin(2*pi*location.y) - theta1/theta2*exp(theta2*state.u(1,:) - 1);
end

Or as a simple function handle:

c = 1;
a = 1;
theta1 = 0.1;
theta2 = 0.1;
fun = @(location,state,theta1,theta2) 100*sin(2*pi*location.x).*sin(2*pi*location.y) - theta1/theta2*exp(theta2*state.u - 1);
f = @(location,state) fun(location,state,theta1,theta2);
specifyCoefficients(model,"m",0,"d",0,"c",c,"a",a,"f",f);