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

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sonu kumar
sonu kumar on 14 Jan 2020
Commented: sonu kumar on 18 Jan 2020
% -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!
  2 Comments
sonu kumar
sonu kumar on 14 Jan 2020
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.

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Accepted Answer

Jyotsna Talluri
Jyotsna Talluri on 17 Jan 2020
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

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