Hi everybody, I need help in fixing my error for the matlab code

% -d^2f(x)/dx^2 = 3+2*x^2;

clc;
clear all;
close all;
syms k(x) ;
k(x) = 3 +2*x^2;  % known  fn
nb = 4;   % selection of heighest no of basis fn
%% Analytical solution
 syms g(x)
 eqn = -diff(g(x),2) == 3 +2*x^2; % diff eqn
 cond = [g(0)==0, g(1)==0];  % boundary cond
 a(x) = dsolve(eqn,cond); % diff soln

 %% calculating z_matrix and v_vector 
 % Numerical solution %
for N = 2:nb
    z = zeros(2,2);
    v = zeros(1,2);
    for n = 1:N
        b(n) = (x-(x^(n+1))); %  basis fn 
        w(n) = b(n);       % galerkin's MOM
        l(n) = -diff(b(n),x,2);   % operator L
        kr(n) = w(n).*k;      % inner product
        v(n) = int(kr(n),[0 1]); % v_vector using inner product b/w x->0 to 1
    end     
      for i = 1:N
        for j = 1:N
            pr(i,j) = w(i).*l(j);
            z(i,j) = int(pr(i,j),[0 1]); % z_matrix
        end
      end

%% LU_decomposition using gauss_elimination
zv = [z v'];
L = eye(N,N);
   for i = 2:1:N
       alpha(i,1) = zv(i,1)/zv(1,1);  
       L(i,1) = alpha(i,1);  % L_matrix elements
       zv(i,:) = zv(i,:)- (alpha(i,1)*zv(1,:)); % making zeros in col 1 using pivot 1
   end
   for r = 3:1:N
       alpha(r,2) = zv(r,2)/zv(2,2); 
       L(r,2) = alpha(r,2);
       zv(r,:) = zv(r,:)-(alpha(r,2)*zv(2,:)); % making zero in col 2 using pivot 2
    end
U = zv(1:N,1:N);
%% using dummy variable_y finding_I 
zb = [L v']; % Augmented matrix
y = zeros(N,1);
y(1) = zb(1,end)/zb(1,1);
  for p = 2:1:N
      y(p) = (zb(p,end)-(zb(p,1:p-1)*y(1:p-1)))/zb(p,p); % forward substitution
  end
I = zeros(N,1);
I(N) = y(N)/U(N,N);  % I_vector calculation
  for q = N-1:-1:1
      I(q) = (y(q)-(U(q,2:N)*I(2:N)))/U(q,q);
  end
  
  f(N) = b*I ; %finding f(x)
end
for h = 2:nb   
    figure(h)
    d(x) = f(h);
    x = 0:0.01:1;
    plot(x,d(x),'b-','linewidth',2);
    hold on
    grid on
    plot(x,a(x),'r-','linewidth',1);
    xlabel('x')
    ylabel('f(x)')
    legend('Numerical method','Analytical method')
end

I have ' f ' as a vector of different functions and I want to plot is simultaneously in different figures but I'm not able to do it, error is showing ''Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variablesand function body must be sym expression''. But when I ommitting the loop in plot and by separate plotting I'm getting the plot for each h = 2/3/4. So please help me how to fix this problem.

Thank you for your help!

[KALYAN ACHARJYA]

k(x) ?? Its represents indexing, not a function of x in MATLAB

[sonu kumar]

Thank you for your comment!

K(x) is known function of diffrential eqn and again I need this function while taking function inner product with weighting fn " w ".If I'm considering indexing at beginning it again showing error.

Answer 1

[Jyotsna Talluri]

Here,f(h) is a symbolic expression and not a symfun and is assigned to a variable d,Hence you have to use subs(d,x) inorder to get the value of d at x

for h = 2:nb   
    figure(h)
    d = f(h);
    x = 0:0.01:1;
    plot(x,subs(d,x),'b-','linewidth',2);
    hold on
    grid on
    plot(x,a(x),'r-','linewidth',1);
    xlabel('x')
    ylabel('f(x)')
    legend('Numerical method','Analytical method')
    hold off;
end

[sonu kumar]

Thank you!

Code is working now.