3 views (last 30 days)

I am using dsolve function in MATLAB to solve a differential equation. It is so slow and can not end up with a result. Is there a way to speed it up, or is there another way for solving a differential equation? I don't want to solve it numerically.

The equations are as follow:

all the derivatives in above equations are replaced with equivalent expressions, so all are only function of y and T only.

I need to solve this equation:

Cg, Cs and qi are constants. The initial conditions for positive root is (y=0.01, T=0) and for negative root is (y=0.99, T=0).

Here is my code:

R=1.9872; %cal/mol/K

eps=0.763;

rhos=0.484; %gr/cm3

T0=300; %theta K

y0=0.01;

ys=0.99;

p=1; %atm

Upg=0.68e-3; %mol/cm2/s

L=100; %cm column length

Cg=1.04*239.006/1000*28.0134; % kj/kg/k to cal/mol/k N2

Cs=0.22; %cal/gr/k

% m(mol/gr) b(1/atm) q(cal/mol)

cA=[3.65e-3 2.8e-4 4900]; % co2 BPL AC

cB=[3.65e-3 13.5e-4 2500]; % N2 BPL AC

i=1;

IPA=cA(i,:); IPB=cB(i,:);

IPA1=IPA(1);IPA2=IPA(2);IPA3=IPA(3);

IPB1=IPB(1);IPB2=IPB(2);IPB3=IPB(3);

syms T(y)

DN1T= @(y,T) (IPA1*IPA2*p*y*exp(IPA3/(R*(T + T0)))*((IPA2*IPA3*p*y*exp(IPA3/(R*(T + T0))))/(R*(T + T0)^2) - (IPB2*IPB3*p*exp(IPB3/(R*(T + T0)))...

*(y - 1))/(R*(T + T0)^2)))/(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)^2 -...

(IPA1*IPA2*IPA3*p*y*exp(IPA3/(R*(T + T0))))/(R*(T + T0)^2*(IPA2*p*y*exp(IPA3/(R*(T + T0))) - ...

IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1));

DN2T =@(y,T) (IPB1*IPB2*IPB3*p*exp(IPB3/(R*(T + T0)))*(y - 1))/(R*(T + T0)^2*(IPA2*p*y*exp(IPA3/(R*(T + T0))) - ...

IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)) - (IPB1*IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1)*((IPA2*IPA3*p*y*...

exp(IPA3/(R*(T + T0))))/(R*(T + T0)^2) - (IPB2*IPB3*p*exp(IPB3/(R*(T + T0)))*(y - 1))/(R*(T + T0)^2)))...

/(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)^2;

DN1Y =@(y,T) (IPA1*IPA2*p*exp(IPA3/(R*(T + T0))))/(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)...

- (IPA1*IPA2*p*y*exp(IPA3/(R*(T + T0)))*(IPA2*p*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))))/...

(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)^2;

DN2Y =@(y,T) (IPB1*IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1)*(IPA2*p*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))))/...

(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1)^2 - (IPB1*IPB2*p*exp(IPB3/(R*(T + T0))))...

/(IPA2*p*y*exp(IPA3/(R*(T + T0))) - IPB2*p*exp(IPB3/(R*(T + T0)))*(y - 1) + 1);

A=@(y,T) Cg*(DN1T(y,T)-y*(DN1T(y,T)+DN2T(y,T)));

B=@(y,T) (Cg*(T)*(DN1T(y,T)+DN2T(y,T))-Cs)+Cg*(DN1Y(y,T)-y*(DN1Y(y,T)+DN2Y(y,T)))+cA(i,3)*DN1T(y,T)+cB(i,3)*DN2T(y,T);

C=@(y,T) Cg*(T)*(DN1Y(y,T)+DN2Y(y,T))+cA(i,3)*DN1Y(y,T)+cB(i,3)*DN2Y(y,T);

S4=@(y,T) (-B(y,T) +(B(y,T) ^2-4*A(y,T) *C(y,T) )^0.5)/2/A(y,T) ;

S2=@(y,T) (-B(y,T) -(B(y,T) ^2-4*A(y,T) *C(y,T) )^0.5)/2/A(y,T) ;

S4sol=dsolve([diff(T,y)==S4(y,T) , T(y0)==0])

S2sol=dsolve([diff(T,y)==S2(y,T) , T(ys)==0])

Kiran Felix Robert
on 8 Oct 2020

Hi Leila,

One way to speed-up the execution is to add a limit on the maximum degree of radicals. The following shows you an example,

S = dsolve(..,'MaxDegree',2);

This will force dsolve to assume implicit formulas for polynomials of degree greater than the specified value.

Kiran Felix Robert

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
## 5 Comments

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036435

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036435

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036450

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036450

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036525

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036525

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036744

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036744

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036789

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/604957-another-function-for-solving-differential-equation-other-than-dsolve-in-matlab#comment_1036789

Sign in to comment.