help me what is the error in the code not able to plot

% current density equation    j=dv/dx=0 at x=0
alpha = 0.1;
gamma =[1,50,100,500,1000];
epsilon = 1;
a=1000;
%% u=y(1)
%% v=y(2)
%% du/dx=dy(1)/dx=y(3)
%%d^2u/dx^2=dy(3)/dx=gamma*y(1)/(1+alpha*y(1)
%% dv/dx=dy(2)/dx=y(4)
%% d^2v/dx^2=dy(4)/dx=a*delta_v*y(4)-(2/epsilon)*gamma*y(1)/(1+alpha*y(1)
figure
hold on;

for i = 1:numel(gamma)
    fcn = @(x, y) [y(3); y(4); (gamma(i) * y(1)) / (1 + alpha * y(1)); a * sol.y(2, x) * y(4) - (2 / epsilon) * (gamma(i) * y(1)) / (1 + alpha * y(1))];
    bc = @(ya, yb) [ya(1) - 1; ya(2); yb(3); yb(4)];
    guess = @(x) [1; 0; 0; 0];
    xmesh = linspace(0, 1, 20);
    solinit = bvpinit(xmesh, guess);
    sol = bvp4c(fcn, bc, solinit, [], gamma(i));
    voltage_drop_values = sol.y(2, :);
    current_density_values = sol.y(4, :);
    plot(voltage_drop_values, current_density_values);
end

Error using solution>@(x,y)[y(3);y(4);(gamma(i)*y(1))/(1+alpha*y(1));a*sol.y(2,x)*y(4)-(2/epsilon)*(gamma(i)*y(1))/(1+alpha*y(1))]
Too many input arguments.

Error in bvparguments (line 96)
testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);

xlabel('Normalized voltage drop across the cell (delta_v*)');
ylabel('Normalized current density at the boundary condition for dv/dx at x=0');
title('Plot of normalized current density at the boundary condition for dv/dx at x=0 versus gamma');
legend('\gamma = 1', '\gamma = 50', '\gamma = 100', '\gamma = 500', '\gamma = 1000');
hold off;
grid on;
xlim([1e-4, 1e2]);
ylim([0, 70]);

[Anitha]

I request any one to help me to solve this program

Answer 1

[Ishu]

Hi Anitha,

Given your clarification about the error, it is occurring with the "bvp4c" function due to "Too many input arguments".

The "bvp4c" function in MATLAB is used to solve Boundary Value Problems (BVP) for Ordinary Differential Equations (ODE). Its basic usage is as follows:

sol = bvp4c(odefun, bcfun, solinit, options);

Based on your description, there was an attempt to pass five arguments to "bvp4c", which exceeds its limit of four arguments, thus leading to the "Too many input arguments" error. To correct this, ensure you are using "bvp4c" correctly by adjusting the call to include only the necessary arguments.

If you have additional parameters that need to be passed into your function, you need to ensure these are encapsulated within those function definitions, possibly using anonymous functions or nested functions that have access to the additional parameters.

sol = bvp4c(fcn, bc, solinit);

The usage of "sol.y(2,x)" in "fcn" is incorrect because "x" is not an index; it will result in an error. To correct this, you can use "deval" instead.

deval(sol, x, 2); %Replace with sol.y(2,x);

You can refer below documentations for more information:

"bvp4c" - https://www.mathworks.com/help/matlab/ref/bvp4c.html#:~:text=odefun%2Cbcfun%2Csolinit)-,sol%20%3D%20bvp4c(odefun%2Cbcfun%2Csolinit%2Coptions),-Description

"deval" - https://www.mathworks.com/help/matlab/ref/deval.html#:~:text=y%20%3D%20deval(sol%2Cx)%20and%20y%20%3D%20deval(x%2Csol)%20evaluate%20the%20solution%20sol%20of%20a%20differential%20equation%20problem%20at%20the%20points%20contained%20in%20x.

Hope it helps!