Function file with more than one out put and how to use that function file for two different output

I have a function

and its derivative

Now I want to creat a function file with both the output so that i can creat one new function file with formula

the function file I created is showing the following error

%%%%%%%%%%%%%%%%%%%%%%%%%%function fils are as follows :

%%%%%%%%%%%%%%%%%%%% f.m %%%%%%

function V = f(x)

V = x^2/2;

end

%%%%%%%%%%%%%%%%%%% %%%

function V = f1(x)

V1= x^2/2;

V=diff(V1,x,1)

end

%%%%%%%%%%%%% FluxR.m %%%

function V = FluxR(a,b)

V = 0.5*(f(a)+f(b))-0.5*max(abs(f1(a)),abs(f1(b)))*(b-a)

end

All the files are kept in the same folder

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x0 = -1;

xf = 1;

N = 50;

h = (xf-x0)/N;

delt = 0.5*h;

lambda = delt/h;

t0 = 0;

tf = 1;

x = zeros(N-1,1);

u0 = zeros(N-1,1);

for j=1:N-1

x(j) = x0+j*h;

if(x(j) <0)

u0(j) =1;

end

if(x(j) > 0)

u0(j) = 0;

end

end

M = fix((tf-t0)/delt);

unew = zeros(N-1,1);

t = t0;

for k=1

unew(1) = u0(1);

unew(N-1) = u0(N-1);

for j=2:N-2

m= u0(j)

lambda

FluxR(u0(j),u0(j+1))

FluxR(u0(j-1),u0(j))

%unew(j) = u0(j) - lambda*(FluxR(u0(j),u0(j+1)) - FluxR(u0(j-1),u0(j)))

end

% plot(x,unew)

% u0 = unew;

% t = t+delt;

end

when I call the function file its showing the following error

Error using diff

Difference order N must be a positive integer scalar.

Error in f1 (line 3)

V=diff(V1,x,1)

Error in FluxR (line 2)

V = 0.5*(f(a)+f(b))-0.5*max(abs(f1(a)),abs(f1(b)))*(b-a)

Error in rs (line 32)

FluxR(u0(j),u0(j+1))

Answer 1

[Niranjan Sundararajan]

Hey there,

From what I understand, you are having trouble calculating the first order differential of x^2/2. That is why you are getting the error. In order to solve this, you can simply use the following script:

t = 5; %example
[out, diff_out] = f(t)

ou = 

diff_out = 

5

function [V, V1] = f(t)
syms x;
func = x^2/2; 
diff_func = diff(func, x);
V = subs(func, x, t);
V1 = subs(diff_func, x, t);
end

This way, in one function itself, you get both f and the differential of f, for any input value of t.