Error while Solving Integral Differential Equation using Dsolve
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I am trying to solve the Basset Boussinesq oseen Equation with Mei Adrian kernel. This is an equation which contains the velocity of the particle, velocity of fluid, differential of velocity for particle and fluid and integral of differential of velocity of particle and fluid in an Integro Differential Equation. All the said variables vary with time t. This is the 1st time I'm trying this in Matlab and Im getting the Following Error
Undefined function or variable 't'.
Error in Code (line 26) cond1=t==20*pi;
How do i circumvent or solve this? t is meant to be a variable here and that is why i gave the Boundary condition till t =20*pi;
Thank you for your support in this regard, I have enclosed the entire code below.
syms v uc t s l
rop=[1000,2650,1];
rof=[1,1000,1000];
dp=0.001;
uf=[1.81*10^-5,8.9*10^-4,8.9*10^-4];
uc=0;
v=@t;
V=1/6*pi*(dp^3);
for i=1:3
mf(i)=rof(i)*V;
mp(i)=rop(i)*V;
g=9.81;
Fun=@(t) mf(i)*diff(uc,t)-mf(i)*g;
Fqs=@(t) 3*pi*uf*dp*(uc-v);
Fvs=@(t) 0.5*mf(i)*(diff(uc,t)-diff(v,t));
Re=@(t) rof(i)*v*dp/uf(i);
tu=@(t) (4/pi)^1/3*dp^2/(uf(i)/rof(i))*((0.75+0.105*Re)/Re)^2;
kernel=@(l) 1/tu*(1/(l/tu)^0.25+(l/tu))^2;
fk=@(s)(kernel(t-s)*(diff(uc,t)-diff(v,t)));
a1=1.5*dp^2*rof(i);
b1=(pi*uf(i)/rof(i))^0.5;
c1=@(t) int(fk,-inf,t);
Fvu=@(t) a1*b1*c1;
F=@(t) mp(i)*diff(v,t);
F1=@(t) Fun+Fqs+Fvs+Fvu;
cond=t=0:0.01:20*pi;
cond=v(0)==0;
eqn=F1(t)==F(t);
dsolve(eqn,cond,cond1)
end
1 个评论
Torsten
2017-4-6
Please include your problem in the usual mathematical notation.
Nobody in the forum will try to assemble all the functions you use in order to finally arrive at "eqn".
Best wishes
Torsten.
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