Clear Filters
Clear Filters

i have error in runge kutta 4 order.

4 views (last 30 days)
Rashmi
Rashmi on 13 Jun 2024
Edited: Walter Roberson on 16 Jun 2024
Alpha1=1;
Alpha2=2;
S=1;
omega=1
omega = 1
gamma=1;
Sc=1;
Pr=1.0;
f_omega=0.4;
zeta=0;
k = 0.1;
h=0.05; % step size
eta = 0:h:100; % Calculates upto y(3)
H = zeros(1,length(eta));
g = zeros(1,length(eta));
F = zeros(1,length(eta));
z = zeros(1,length(eta));
G = zeros(1,length(eta));
x = zeros(1,length(eta));
theta = zeros(1,length(eta));
y = zeros(1,length(eta));
phi = zeros(1,length(eta));
F(1) = 0;
G(1) = omega;
theta(1) = 1;
phi(1) = 1;
H(1) = S +f_omega / Sc * y(1) ;
u1 = @(eta, H) (-2*F);
u2 = @(eta,F) g;
u3 = @(eta,F,g) (g*H - G.^2 +F.^2 - S(((eta+1)/2)*g + F) + k(z.^2 -g.^2)) / (1-2*F*k);
u4 = @(eta,G) z;
u5 = @(eta,G,z) ((H*z + 2*F*G - S(((eta+1)/2)*z + G) - 2*k*g*z)/(1-2*F*k));
u6 = @(eta, theta) x;
u7 = @(eta, theta , x) (Pr*(H*x + S(((rta+1)/2)*x + alpha1*theta) - 2*zeta*F*H*x)/(1-Pr*zeta));
u8 = @(eta, phi) y ;
u9 = @(eta, phi, y) (Sc*(H*y - S(((eta+1)/2)*y + alpha2*phi) +gamma*phi));
for i=1:(length(eta)-1) % calculation loop
k_1 =u1(eta(i),H(i));
l_1 =u2(eta(i),F(i));
m_1 =u3(eta(i),F(i),g(i));
n_1 =u4(eta(i),G(i));
o_1 =u5(eta(i),G(i),z(i));
p_1 =u6(eta(i),theta(i));
q_1 =u7(eta(i),theta(i),x(i));
r_1 =u8(eta(i),phi(i));
s_1 =u9(eta(i),phi(i),y(i));
k_2 = u1(eta(i)+0.5*h,H(i)+0.5*h*k_1);
l_2 = u2(eta(i)+0.5*h,F(i)+0.5*h*l_1);
m_2 = u3(eta(i)+0.5*h,F(i)+0.5*h*l_1,g(i)+0.5*h*m_1);
n_2 = u4(eta(i)+0.5*h,G(i)+0.5*h*n_1);
o_2 = u5(eta(i)+0.5*h,G(i)+0.5*h*n_1,z(i)+0.5*h*o_1);
p_2 = u6(eta(i)+0.5*h,theta(i)+0.5*h*p_1);
q_2 = u7(eta(i)+0.5*h,theta(i)+0.5*h*p_1,x(i)+0.5*h*q_1);
r_2 = u8(eta(i)+0.5*h,phi(i)+0.5*h*r_1);
s_2 = u9(eta(i)+0.5*h,phi(i)+0.5*h*r_1,x(i)+0.5*h*s_1);
k_3 = u1(eta(i)+0.5*h,H(i)+0.5*h*k_2);
l_3 = u2(eta(i)+0.5*h,F(i)+0.5*h*l_2);
m_3 = u3(eta(i)+0.5*h,F(i)+0.5*h*l_2,g(i)+0.5*h*m_2);
n_3 = u4(eta(i)+0.5*h,G(i)+0.5*h*n_2);
o_3 = u5(eta(i)+0.5*h,G(i)+0.5*h*n_2,z(i)+0.5*h*o_2);
p_3 = u6(eta(i)+0.5*h,theta(i)+0.5*h*p_2);
q_3 = u7(eta(i)+0.5*h,theta(i)+0.5*h*p_2,x(i)+0.5*h*q_2);
r_3 = u8(eta(i)+0.5*h,phi(i)+0.5*h*r_2);
s_3 = u9(eta(i)+0.5*h,phi(i)+0.5*h*r_2,x(i)+0.5*h*s_2);
k_4 = u1(eta(i)+h,H(i)+h*k_3);
l_4 = u2(eta(i)+h,F(i)+h*l_3);
m_4 = u3(eta(i)+h,F(i)+h*l_3,g(i)+h*m_3);
n_4 = u4(eta(i)+h,G(i)+h*n_3);
o_4 = u5(eta(i)+h,G(i)+h*n_3,z(i)+h*o_3);
p_4 = u6(eta(i)+h,theta(i)+0.5*h*p_2);
q_4 = u7(eta(i)+h,theta(i)+h*p_3,x(i)+h*q_3);
r_4 = u8(eta(i)+h,phi(i)+h*r_3);
s_4 = u9(eta(i)+h,phi(i)+h*r_3,x(i)+h*s_3);
H(i+1) = H(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;
g(i+1) = g(i) + (1/6)*(l_1+2*l_2+2*l_3+l_4)*h;
F(i+1) = F(i) + (1/6)*(m_1+2*m_2+2*m_3+m_4)*h;
z(i+1) = z(i) + (1/6)*(n_1+2*n_2+2*n_3+n_4)*h;
G(i+1) = G(i) + (1/6)*(o_1+2*o_2+2*o_3+o_4)*h;
x(i+1) = x(i) + (1/6)*(p_1+2*p_2+2*p_3+p_4)*h;
theta(i+1) = theta(i) + (1/6)*(q_1+2*q_2+2*q_3+q_4)*h;
y(i+1) = y(i) + (1/6)*(r_1+2*r_2+2*r_3+r_4)*h;
phi(i+1) = phi(i) + (1/6)*(s_1+2*s_2+2*s_3+s_4)*h;
end
Array indices must be positive integers or logical values.

Error in solution>@(eta,F,g)(g*H-G.^2+F.^2-S(((eta+1)/2)*g+F)+k(z.^2-g.^2))/(1-2*F*k) (line 31)
u3 = @(eta,F,g) (g*H - G.^2 +F.^2 - S(((eta+1)/2)*g + F) + k(z.^2 -g.^2)) / (1-2*F*k);
figure();
subplot(3,2,1);
plot(eta, F);
title('F vs \eta');
xlabel('\eta');
ylabel('F');
subplot(3,2,2);
plot(eta, G);
title('G vs \eta');
xlabel('\eta');
ylabel('G');
subplot(3,2,3);
plot(eta, theta);
title('\theta vs \eta');
xlabel('\eta');
ylabel('\theta');
subplot(3,2,4);
plot(eta, phi);
title('\phi vs \eta');
xlabel('\eta');
ylabel('\phi');
subplot(3,2,5);
plot(eta, H);
title('H vs \eta');
xlabel('\eta');
ylabel('H');
error
Array indices must be positive integers or logical values.

Answers (1)

Ganesh
Ganesh on 13 Jun 2024
The error occurs as you are trying to index the variable "S" while calling function "u3" whereas you have declared S to be an integer value of 1.
u3 = @(eta,F,g) (g*H - G.^2 +F.^2 - S(((eta+1)/2)*g + F) + k(z.^2 -g.^2)) / (1-2*F*k);
  2 Comments
Rashmi
Rashmi on 16 Jun 2024
No S not a function in this line I am forget *.
Torsten
Torsten on 16 Jun 2024
Edited: Torsten on 16 Jun 2024
u1 = @(eta, H) (-2*F);
u2 = @(eta,F) g;
u3 = @(eta,F,g) (g*H - G.^2 +F.^2 - S(((eta+1)/2)*g + F) + k(z.^2 -g.^2)) / (1-2*F*k);
u4 = @(eta,G) z;
u5 = @(eta,G,z) ((H*z + 2*F*G - S(((eta+1)/2)*z + G) - 2*k*g*z)/(1-2*F*k));
u6 = @(eta, theta) x;
u7 = @(eta, theta , x) (Pr*(H*x + S(((rta+1)/2)*x + alpha1*theta) - 2*zeta*F*H*x)/(1-Pr*zeta));
u8 = @(eta, phi) y ;
u9 = @(eta, phi, y) (Sc*(H*y - S(((eta+1)/2)*y + alpha2*phi) +gamma*phi));
Why don't you define u1 to depend on F ? You only make it depend on eta and H.
Why don't you define u2 to depend on g ?
Why don't you define u3 to depend on G and H ?
...

Sign in to comment.

Tags

Products


Release

R2024a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!