"Symbolic parameters not supported in nonpolynomial equations"

clc;

clear all;

close all;

syms a b d y c

x = 0.1; %leading egde distance (in cm)

Re = 1000; %Reynolds number

delta = (5*x)/(Re^(1/2)); %Boundary layer thickness

nu = 8.926e-03; %kinematic viscosity (in cm2./s)

U_inf = (Re*nu)/x; %freestream velocity(in cm./s)

alpha = 1:1:20; %wave number (in 1./cm)

U(y) = a*y^2 + b*y + d; %velocity profile equation

DU(y) = diff(U(y),y);

eqn1 = U(0)==0; %boundary condition1

eqn2 = U(delta)==U_inf; %boundary condition2

eqn3 = DU(delta)==0; %boundary condition3

eqns = [eqn1 eqn2 eqn3];

soln = solve(eqns,a,b,d);

a = double(soln.a); %value of a in velocity profile (in 1./cm.s)

b = double(soln.b); %value of b in velocity profile (in 1./s)

d = double(soln.d); %value of d in velocity profile (in cm./s)

z = delta./2; %location of y

u = double(subs(a*z^2 + b*z + d));

ddu = double(2*a);

%Non-dimensionalizing

Uy = double(u./U_inf);

ddUy = double((ddu.*delta.^2)./U_inf);

A = double(alpha.*delta);

Y = z./delta;

%Roots of the OS equation

C = zeros(1,length(alpha));

for i=1:1:20

l1(i) = -((-((A(i).*Re.*c.*1i)-(2.*A(i).^2)-(A(i).*Re.*Uy.*1i))+((2.*A(i).^2.*Re.^2.*Uy.*c)-(A(i).^2.*Re.^2.*(Uy.^2+c.^2))-(4.*A(i).*Re.*ddUy.*1i)).^(1/2))/2).^(1./2);

l2(i) = -((-((A(i).*Re.*c.*1i)-(2.*A(i).^2)-(A(i).*Re.*Uy.*1i))-((2.*A(i).^2.*Re.^2.*Uy.*c)-(A(i).^2.*Re.^2.*(Uy.^2+c.^2))-(4.*A(i).*Re.*ddUy.*1i)).^(1/2))/2).^(1/2);

LHS = ((Uy-c).*((l1(i).^2.*exp(l1(i).*y) - l2(i).^2.*exp(l2(i).*y)) - (a(i).^2.*(exp(l1(i).*y)-exp(l2(i).*y))))-(ddUy.*(exp(l1(i).*y)-exp(l2(i).*y))));

RHS = ((1/(a(i).*Re.*1i)).*(((l1(i).^4.*exp(l1(i).*y))-(l2(i).^4.*exp(l2(i).*y)))-(2.*a(i).^2.*(l1(i).^2.*exp(l1(i).*y) - l2(i).^2.*exp(l2(i).*y))) + a(i).^4.*(exp(l1(i).*y)-exp(l2(i).*y))));

eqn(i) = LHS-RHS;

C(i) = vpasolve(simplify(eqn(i)),c);

end

disp(C)

There is error inside the for loop. Can somebody help?

Thanks!!

Answer 1

[Walter Roberson]

C(i) = vpasolve(simplify(eqn(i)),c);

At that point in the code the equation involves more variables than just c, so you have more variables than equations.

vpasolve can handle more variables than equations only for polynomials, in which case it does the equivalent of solve() followed by vpa(), returning roots that involve the other variables.

[Maya Venugopalan]

So what should I do? I'm getting "Symbolic parameters not supported in nonpolynomial equations." again.

[Maya Venugopalan]

When I tried to separate the for loop, I got the answer. But that too different values of c using different programs.

clc;

clear all;

close all;

syms c

delta = 0.0158;

alp = 1:1:20;

a = alp.*delta;

Re = 1000;

y = 0.5;

y1 = y.*delta;

U = (-357554.879.*y1.^2 + 11298.734.*y1)./89.26;

ddU = -2;

C = zeros(1,length(alp));

for i=1:1:20

l3(i) = -((-((a(i).*Re.*c.*1i)-(2.*a(i).^2)-(a(i).*Re.*U.*1i))+((2.*a(i).^2.*Re.^2.*U.*c)-(a(i).^2.*Re.^2.*(U.^2+c.^2))-(4.*a(i).*Re.*ddU.*1i)).^(1./2))./2).^(1./2);

l4(i) = -((-((a(i).*Re.*c.*1i)-(2.*a(i).^2)-(a(i).*Re.*U.*1i))-((2.*a(i).^2.*Re.^2.*U.*c)-(a(i).^2.*Re.^2.*(U.^2+c.^2))-(4.*a(i).*Re.*ddU.*1i)).^(1./2))./2).^(1./2);

LHS = ((U-c).*((l3(i).^2.*exp(l3(i).*y) - l4(i).^2.*exp(l4(i).*y)) - (a(i).^2.*(exp(l3(i).*y)-exp(l4(i).*y))))-(ddU.*(exp(l3(i).*y)-exp(l4(i).*y))));

RHS = ((1./(a(i).*Re.*1i)).*(((l3(i).^4.*exp(l3(i).*y))-(l4(i).^4.*exp(l4(i).*y)))-(2.*a(i).^2.*(l3(i).^2.*exp(l3(i).*y) - l4(i).^2.*exp(l4(i).*y))) + a(i).^4.*(exp(l3(i).*y)-exp(l4(i).*y))));

eqn(i) = LHS-RHS;

C(i) = vpasolve(simplify(eqn(i)),c);

end

disp(C)

This gives me solutions properly. But not as same values as the first code though. Why is that so?