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Home/Matlab/I have error in FDM 2

I have error in FDM 2

/ 2024-06-23 / Matlab

function FDMex()
N = 100;

h = 0.1;
eta = 0:h:N;
Ac = 0.0001;
S = 0.2;
k = 0.1;
Pr = 1.0;
Sc = 1.2;
alpha1 = 0.4;
alpha2 = 0;
zeta = 0.3;
gamma = 0.3;
omega = 0.4;
fw = 0.2;

F = zeros(N+2, 1);
G = zeros(N+2, 1);
theta = zeros(N+2, 1);
phi = zeros(N+2, 1);
H = zeros(N+2, 1);

F(1) = 0;
G(1) = omega;
theta(1) = 1;
phi(1) = 1;
H(1) = S + fw / Sc * (phi(2) – phi(1)) / h^2;
F(N+2) = 0;
G(N+2) = 0;
theta(N+2) = 0;
phi(N+2) = 0;

c = 1.0;
while(c>0)
[H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h);
c = 0.0;
for j = 1:N+1
if (abs(H(j)-H1(j))>Ac); (abs(F(j)-F1(j))>Ac);(abs(G(j)-G1(j))>Ac);(abs(theta(1)-theta1(1))>Ac);(abs(phi(j)-phi1(j))>Ac);
c = c+1;
break
end
end
H = H1;
F = F1;
G = G1;
theta = theta1;
phi = phi1;
end
disp(‘Hence solutions = :’ );
H2(1 : N+2) = H;
F2(1 : N+2) = F;
G2(1 : N+2) = G;
theta2(1 : N+2) = theta;
phi2(1 : N+2) = phi;
eta = 0:0.1:N;

figure(1)
plot(eta,H2,’*r’)
hold on

function [H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h)
for i = 1:N-1
H(i+1) = H(i) – h*2*F(i);
F(i+1) = (F(i) + F(i+2))/2 -H(i)*(h/2)*(F(i+1)-F(i)) +(h^2)*(G(i)^2) – (h^2)*(F(i)^2) + (h^2)*(S/2)*((((i*h)+1)/2)*((F(i+1)-F(i))/h)+F(i)) – (h^2)*(k/2)*(((G(i+1)-G(i))/h)^2 – ((F(i+1)-F(i))/h)^2+2*F(i)*((F(i) -2*F(i+1) + F(i+2))/h^2));
G(i+1) = (G(i) + G(i+2))/2 -(h/2)*H(i)*(G(i+1)-G(i)) – (h^2)*F(i)*G(i) + (h^2)*S*(((i*h+1)/2)*((G(i+1)-G(i))/h)+G(i)) – (h^2)*k*(F(i)*((G(i) -2*G(i+1) + G(i+2))/h^2) – ((F(i+1)-F(i))/h)*((G(i+1)-G(i))/h));
theta(i+1) = (theta(i) + theta(i+2))/2 – Pr*(h/2)*(theta(i+1)-theta(i))*H(i) + Pr*(h^2)*(S/2)*(((i*h+1)/2)*((theta(i+1)-theta(i))/h)+alpha1*theta(i)) – zeta*Pr*((h^2)/2)*((theta(i) -2*theta(i+1) + theta(i+2))/h^2 – 2*F(i)*H(i)*((theta(i+1)-theta(i))/h));
phi(i+1) = (phi(i) + phi(i+2))/2 + Sc*(h/2)*H(i)*(theta(i+1)-theta(i)) – Sc*(h^2)*(S/2)*(((i*h+1)/2)*((phi(i+1)-phi(i))/2*h)+alpha2*phi(i)) + (Sc/2)*(h^2)*gamma*phi(i);
end
H1(1) = H(1);
F1(1) = F(1);
G1(1) = G(1);
theta1(1) = theta(1);
phi1(1) = phi(1);

F1(N+2) = F(N+2);
G1(N+2) = G(N+2);
theta1(N+2) = theta(N+2);
phi1(N+2) = phi(N+2);
end
end
Index exceeds the number of array elements. Index must not exceed 1. Line 39function FDMex()
N = 100;

h = 0.1;
eta = 0:h:N;
Ac = 0.0001;
S = 0.2;
k = 0.1;
Pr = 1.0;
Sc = 1.2;
alpha1 = 0.4;
alpha2 = 0;
zeta = 0.3;
gamma = 0.3;
omega = 0.4;
fw = 0.2;

F = zeros(N+2, 1);
G = zeros(N+2, 1);
theta = zeros(N+2, 1);
phi = zeros(N+2, 1);
H = zeros(N+2, 1);

F(1) = 0;
G(1) = omega;
theta(1) = 1;
phi(1) = 1;
H(1) = S + fw / Sc * (phi(2) – phi(1)) / h^2;
F(N+2) = 0;
G(N+2) = 0;
theta(N+2) = 0;
phi(N+2) = 0;

c = 1.0;
while(c>0)
[H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h);
c = 0.0;
for j = 1:N+1
if (abs(H(j)-H1(j))>Ac); (abs(F(j)-F1(j))>Ac);(abs(G(j)-G1(j))>Ac);(abs(theta(1)-theta1(1))>Ac);(abs(phi(j)-phi1(j))>Ac);
c = c+1;
break
end
end
H = H1;
F = F1;
G = G1;
theta = theta1;
phi = phi1;
end
disp(‘Hence solutions = :’ );
H2(1 : N+2) = H;
F2(1 : N+2) = F;
G2(1 : N+2) = G;
theta2(1 : N+2) = theta;
phi2(1 : N+2) = phi;
eta = 0:0.1:N;

figure(1)
plot(eta,H2,’*r’)
hold on

function [H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h)
for i = 1:N-1
H(i+1) = H(i) – h*2*F(i);
F(i+1) = (F(i) + F(i+2))/2 -H(i)*(h/2)*(F(i+1)-F(i)) +(h^2)*(G(i)^2) – (h^2)*(F(i)^2) + (h^2)*(S/2)*((((i*h)+1)/2)*((F(i+1)-F(i))/h)+F(i)) – (h^2)*(k/2)*(((G(i+1)-G(i))/h)^2 – ((F(i+1)-F(i))/h)^2+2*F(i)*((F(i) -2*F(i+1) + F(i+2))/h^2));
G(i+1) = (G(i) + G(i+2))/2 -(h/2)*H(i)*(G(i+1)-G(i)) – (h^2)*F(i)*G(i) + (h^2)*S*(((i*h+1)/2)*((G(i+1)-G(i))/h)+G(i)) – (h^2)*k*(F(i)*((G(i) -2*G(i+1) + G(i+2))/h^2) – ((F(i+1)-F(i))/h)*((G(i+1)-G(i))/h));
theta(i+1) = (theta(i) + theta(i+2))/2 – Pr*(h/2)*(theta(i+1)-theta(i))*H(i) + Pr*(h^2)*(S/2)*(((i*h+1)/2)*((theta(i+1)-theta(i))/h)+alpha1*theta(i)) – zeta*Pr*((h^2)/2)*((theta(i) -2*theta(i+1) + theta(i+2))/h^2 – 2*F(i)*H(i)*((theta(i+1)-theta(i))/h));
phi(i+1) = (phi(i) + phi(i+2))/2 + Sc*(h/2)*H(i)*(theta(i+1)-theta(i)) – Sc*(h^2)*(S/2)*(((i*h+1)/2)*((phi(i+1)-phi(i))/2*h)+alpha2*phi(i)) + (Sc/2)*(h^2)*gamma*phi(i);
end
H1(1) = H(1);
F1(1) = F(1);
G1(1) = G(1);
theta1(1) = theta(1);
phi1(1) = phi(1);

F1(N+2) = F(N+2);
G1(N+2) = G(N+2);
theta1(N+2) = theta(N+2);
phi1(N+2) = phi(N+2);
end
end
Index exceeds the number of array elements. Index must not exceed 1. Line 39 function FDMex()
N = 100;

h = 0.1;
eta = 0:h:N;
Ac = 0.0001;
S = 0.2;
k = 0.1;
Pr = 1.0;
Sc = 1.2;
alpha1 = 0.4;
alpha2 = 0;
zeta = 0.3;
gamma = 0.3;
omega = 0.4;
fw = 0.2;

F = zeros(N+2, 1);
G = zeros(N+2, 1);
theta = zeros(N+2, 1);
phi = zeros(N+2, 1);
H = zeros(N+2, 1);

F(1) = 0;
G(1) = omega;
theta(1) = 1;
phi(1) = 1;
H(1) = S + fw / Sc * (phi(2) – phi(1)) / h^2;
F(N+2) = 0;
G(N+2) = 0;
theta(N+2) = 0;
phi(N+2) = 0;

c = 1.0;
while(c>0)
[H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h);
c = 0.0;
for j = 1:N+1
if (abs(H(j)-H1(j))>Ac); (abs(F(j)-F1(j))>Ac);(abs(G(j)-G1(j))>Ac);(abs(theta(1)-theta1(1))>Ac);(abs(phi(j)-phi1(j))>Ac);
c = c+1;
break
end
end
H = H1;
F = F1;
G = G1;
theta = theta1;
phi = phi1;
end
disp(‘Hence solutions = :’ );
H2(1 : N+2) = H;
F2(1 : N+2) = F;
G2(1 : N+2) = G;
theta2(1 : N+2) = theta;
phi2(1 : N+2) = phi;
eta = 0:0.1:N;

figure(1)
plot(eta,H2,’*r’)
hold on

function [H1, F1, G1, theta1, phi1] = equation(H,F,G,theta,phi,N,h)
for i = 1:N-1
H(i+1) = H(i) – h*2*F(i);
F(i+1) = (F(i) + F(i+2))/2 -H(i)*(h/2)*(F(i+1)-F(i)) +(h^2)*(G(i)^2) – (h^2)*(F(i)^2) + (h^2)*(S/2)*((((i*h)+1)/2)*((F(i+1)-F(i))/h)+F(i)) – (h^2)*(k/2)*(((G(i+1)-G(i))/h)^2 – ((F(i+1)-F(i))/h)^2+2*F(i)*((F(i) -2*F(i+1) + F(i+2))/h^2));
G(i+1) = (G(i) + G(i+2))/2 -(h/2)*H(i)*(G(i+1)-G(i)) – (h^2)*F(i)*G(i) + (h^2)*S*(((i*h+1)/2)*((G(i+1)-G(i))/h)+G(i)) – (h^2)*k*(F(i)*((G(i) -2*G(i+1) + G(i+2))/h^2) – ((F(i+1)-F(i))/h)*((G(i+1)-G(i))/h));
theta(i+1) = (theta(i) + theta(i+2))/2 – Pr*(h/2)*(theta(i+1)-theta(i))*H(i) + Pr*(h^2)*(S/2)*(((i*h+1)/2)*((theta(i+1)-theta(i))/h)+alpha1*theta(i)) – zeta*Pr*((h^2)/2)*((theta(i) -2*theta(i+1) + theta(i+2))/h^2 – 2*F(i)*H(i)*((theta(i+1)-theta(i))/h));
phi(i+1) = (phi(i) + phi(i+2))/2 + Sc*(h/2)*H(i)*(theta(i+1)-theta(i)) – Sc*(h^2)*(S/2)*(((i*h+1)/2)*((phi(i+1)-phi(i))/2*h)+alpha2*phi(i)) + (Sc/2)*(h^2)*gamma*phi(i);
end
H1(1) = H(1);
F1(1) = F(1);
G1(1) = G(1);
theta1(1) = theta(1);
phi1(1) = phi(1);

F1(N+2) = F(N+2);
G1(N+2) = G(N+2);
theta1(N+2) = theta(N+2);
phi1(N+2) = phi(N+2);
end
end
Index exceeds the number of array elements. Index must not exceed 1. Line 39 rashmi MATLAB Answers — New Questions

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