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i have error in runge kutta 4 order.

조회 수: 4 (최근 30일)
Rashmi
Rashmi 2024년 6월 13일
편집: Walter Roberson 2024년 6월 16일
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.

답변 (1개)

Ganesh
Ganesh 2024년 6월 13일
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);
  댓글 수: 2
Rashmi
Rashmi 2024년 6월 16일
No S not a function in this line I am forget *.
Torsten
Torsten 2024년 6월 16일
편집: Torsten 2024년 6월 16일
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 ?
...

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