Arrays have incompatible sizes for this operation.

% system of first order differential equation

% y1' = y2;

% y2' = y3;

% y3' = (1-phi).^2.5*[(1-phi)+phi*(rows/rowp)*(y1*y3-y1.^2)-M*y2+lamda*y4*((1-phi)+phi*(rowbetas/rowbetaf))]

% y4' = y5;

% y5' = -(3*N*pr*kf*[(1-phi)+phi*(rowcps/rowcpf)]/(3*N+4)*knf)*y1*y5;

%with boundary condition y1(0) = 0, y2(0)=1, y3(0)=-0.74878322(guess), y4(0) = 1, y5(0)=0.2356(guess)

phi = 0.01;

lamda = 1;

M = 2;

Ec = 2;

N = 1.5;

pr = 6.2;

%copper

rows =8933 ;

ks = 401;

cps =385 ;

rowcps=8933*385;

rowbetas = 8933*1.67*10.^-5;

betas = 1.67*10.^-5;

%alumina

% rows =3970 ;

% ks =40 ;

% cps =765;

%betas = 0.85*10.^-5;

%water

rowf = 997.1;

kf = 0.613;

cpf = 4179;

betaf = 21*10.^-5;

rowbetaf = 997.1*21*10.^-5;

rowcpf = 997.1*4179;

% constants

A1 = (1-phi)+phi*(rows/rowf);

A2 = (1-phi)+phi*(rowbetas/rowbetaf);

A3 = (1-phi)+phi*(rowcps/rowcpf);

A = (1-phi).^2.5;

A4 = -(3*N*pr*kf/(3*N+4)*knf);

knf = kf*(ks+2*kf-2*phi*(kf-ks)/ks+2*kf+phi*(kf-ks));

%% solve ODE-IVP using RK-4 Method

tic;

% range of independent variable η

eta_0 = 0;

eta_max = 5;

% Initial conditions

f0 = 0;

g0 = 1;

h0 = -0.74878322

l0 = 1;

m0 = 0.2356

% Step value Δη

d_eta = 0.001;

N = (eta_max - eta_0)/ d_eta;

err= 1;

%% Initializing solution

eta = eta_0 : d_eta : eta_max; % X coordinate for plot function

while err >10^-9

F = zeros(N+1,3); % f = F(N+1,1) ; g = F(N+1,2) ; h = F(N+1,3) ;

F(1,:) = [f0 g0 h0];

G = zeros(N+1,2);

G(1,:) = [l0 m0]; %l = G(N+1,1); m = G(N+1,2); j let us choose artbitrary for two values

%% Trail using RK-4 Method

for i = 1:N

k11(i,:) = d_eta*[G(i,2) A4*A3*F(i,2)*G(i,2)];

k1(i,:) = d_eta* [F(i,2) F(i,3) A*(A1*(F(i,1)*F(i,3)-F(i,2).^2)-M*F(i,2)+lamda*A2*G(i,1))] ;

k12(i,:) = d_eta*[G(i,2)+k11(i,1)/2 A4*A3*F(i,2)+k11(i,:)/2*G(i,2)+k11(i,:)/2];

k2(i,:) = d_eta* [F(i,2)+k1(i,2)/2 F(i,3)+k1(i,3)/2 A*(A1*(F(i,1)+k1(i,1)/2*F(i,3)+k1(i,3)/2-F(i,2).^2+k1(i,2)/2)-M*F(i,2)+k1(i,2)/2+lamda*A2*G(i,1)+k11(i,1)) ];

k13(i,:) = d_eta*[G(i,2)+k12(i,1)/2 A4*A3*F(i,2)+k12(i,:)/2*G(i,2)+k12(i,:)/2];

k3(i,:) = d_eta* [F(i,2)+k2(i,2)/2 F(i,3)+k2(i,3)/2 A*(A1*(F(i,1)+k2(i,1)/2*F(i,3)+k2(i,3)/2-F(i,2).^2+k2(i,2)/2)-M*F(i,2)+k2(i,2)/2+lamda*A2*G(i,1)+k12(i,1)/2) ];

k14(i,:) = d_eta*[G(i,2)+k13(i,1) A4*A3*F(i,2)+k13(i,:)*G(i,2)+k13(i,:)];

k4(i,:) = d_eta* [F(i,2)+k3(i,2) F(i,3)+k3(i,3) A*(A1*(F(i,1)+k3(i,1)*F(i,3)+k3(i,3)-F(i,2).^2+k3(i,2))-M*F(i,2)+k3(i,2)+lamda*A2*G(i,1)+k13(i,1))];

G(i+1,:) = G(i,:)+(1/6)*(k11(i,:)+2*k12(i,:)+2*k13(i,:)+k14(i,:));

F(i+1,:) = F(i,:)+(1/6)*(k1(i,:)+2*k2(i,:)+2*k3(i,:)+k4(i,:));

end

end

%% plotting

f1=figure;

f1.Units = 'normalized';

f1.Position = [0.1 0.1 0.8 0.6];

plot(eta',F,'LineWidth',1);

%plot(eta',G,'Linewidth',1);

got the error :

Arrays have incompatible sizes for this operation.

Error in velocity (line 77)

G(i+1,:) = G(i,:)+(1/6)*(k11(i,:)+2*k12(i,:)+2*k13(i,:)+k14(i,:));

Related documentation

Answer 1

[Muthukumar Ganesan]

Hi,

In the calculation for the highlighted section please index (i,2)

Thanks,

Muthukumar