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can it be possible to use odeVectorField

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MINATI
MINATI on 22 May 2020
Commented: MINATI on 25 May 2020
syms f(x) g(x) h(x) Pr Nb Nt Le
[V] = odeToVectorField( diff(f,3) - diff(f)^2 + f * diff(f,2) == 0,diff(g,2) + Pr * ( f * diff(g) + Nb * diff(g)* diff(h)+ Nt * diff(g)^2) == 0,...
diff(h,2) + Le * f * diff(h) + ( Nt/Nb ) * Pr * ( f * diff(g) + Nb * diff(g)* diff(h)+ Nt * diff(g)^2)== 0)
%% I want to incorporate the expression of [V] into below code, but I am getting wrong expression (not as dydx below)
%%% can it be used in bvp 4c code and in which style
function main
Pr=10; Le=10; Nt=.1;Nb=.1;
xa=0;xb=6;solinit=bvpinit(linspace(xa,xb,1000),[0 1 1 1 0 0 0]);options=[];
sol=bvp4c(@ode,@bc,solinit,options);xint=linspace(xa,xb,100);S=deval(sol,xint);
function res=bc(ya,yb)
res=[ya(1); ya(2)-1; ya(4)-1; ya(6)-1; yb(2); yb(4); yb(6)];
end
function dydx=ode(x,y)
dydx=[y(2); y(3); y(2)^2 - y(3)*y(1); y(5); - Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2);
y(7); - Le*y(7)*y(1) + (Nt/Nb)*Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2)];
end
end
  3 Comments
MINATI
MINATI on 24 May 2020
Please anybody invest some time here to help me.

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Answers (1)

darova
darova on 24 May 2020
Try this
clc,clear
syms f(x) g(x) h(x) x Y
Pr=10;
Le=10;
Nt=.1;
Nb=.1;
[V,y1] = odeToVectorField( diff(f,3) - diff(f)^2 + f * diff(f,2) == 0,...
diff(g,2) + Pr * ( f * diff(g) + Nb * diff(g)* diff(h)+ Nt * diff(g)^2) == 0,...
diff(h,2) + Le * f * diff(h) + ( Nt/Nb ) * Pr * ( f * diff(g) + Nb * diff(g)* diff(h)+ Nt * diff(g)^2)== 0)
F = matlabFunction(V,'vars', [x Y]);
bc = @(ya,yb) [ya(1) % g
ya(2)-1 % Dg
ya(4)-1 % f
ya(6)-1 % Df
yb(2) % D2f
yb(4) % h
yb(6)]; % dh
xa=0;
xb=6;
solinit = bvpinit(linspace(xa,xb,1000),[0 1 1 1 0 0 0]);
options = [];
sol = bvp4c(F,bc,solinit,options);
plot(sol.x,sol.y)
Change boundary conditions if needed
  1 Comment
MINATI
MINATI on 25 May 2020
No dear Darova, its not matching. You can compare also

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