aylin

20 Reputation

3 Badges

10 years, 119 days

MaplePrimes Activity


These are questions asked by aylin

I want to write maple code of the following algorithm with

the following parameters and initial values please help me.

T0 = 5.5556 × 107 cells, I0 = 1.1111 × 107 cells, V0 = 6.3096 × 109 copies/ml,

A1=A2=1,

c = 0.67, h = 1, d = 3.7877 × 10−3, δ = 3.259d,

λ = 2/3× 108d, R0 = 1.33,

p = (cV0δR0)/λ(R0−1)

and β = dδcR0/λp .

 

Algorithm
step 1 :
T(0) = T0, I(0) = I0, V (0) = V0 λi(100 ) = 0 (i=1, ..., 3), u1(0) = 0 =
u2(0).

step 2 :
for i=1, ..., n-1, do :
Ti+1=(Ti + hλ)/(1 + h[d + (1 − u1i)βVi]),

Ii+1 =(Ii + h(1 − u1i)βViTi+1)/(1 + hδ),

Vi+1 =(Vi + h(1 − u2i)pIi+1)/(1 + hc),

λ1n−i−1 =(λ1n−i + h[1 + (1 − u1i)βVi+1])/(1 + h[d + (1 − u1i)βVi+1]),

λ2n−i−1 =(λ2n−i+ hλ3n−i (1 − u2i)p)/(1 + hδ),

λ3n−i−1 =(λ3n−i + h(λ2n−i−1− λ1n−i−1 )(1 − u1i)βTi+1)/(1 + hc),

R1i+1 =(1/A1)(λ1n−i−1−λ2n−i−1 )βVi+1Ti+1,

R2i+1 =−(1/A2)λ3n−i−1 pIi+1,

 

u1i+1 = min(1, max(R1i+1 , 0)),

u2i+1 = min(1, max(R2i+1 , 0)),

end for

 

step 3 :
for i=1, ..., n-1, write
T(ti) = Ti, I(ti) = Ii, V(ti) = Vi,

u1(ti) = u1i, u2(ti) = u2i.

end for

Dear experts;

How can I solve this problem with maple?

restart:


 X[3](0):=6.3096*10^9;
 c:=0.67;
 d:=3.7877*10^(-8);
 delta:=3.259*d;
 lambda:=(2/3)*10^8*d;
 R[0]:=1.33;
 p:=(c*X[3](0)*delta*R[0])/(lambda*(R[0]-1));
beta:=(d*delta*c*R[0])/(lambda*p);

ode:=diff(x[1](t), t)=(lambda-d*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)),
 diff(x[2](t), t) =((1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-delta*x[2](t)),
 diff(x[3](t), t) =((1+psi[3](t)*p*x[2](t)/A[2])*p*x[2](t)-c*x[3](t)),diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*(x[3](t))^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-d+beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
 diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*p^2*x[2](t)+psi[2](t)*delta-psi[3](t)*(psi[3](t)*p^2/A[2]*x[2](t)+(1+psi[3](t)*p*x[2](t)/A[2])*p),
 diff(psi[3](t), t) = 1/A[1]*beta^2*(x[1](t))^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*c;

ics := x[1](0)=5.5556*10^7, x[2](0)=1.1111*10^7,x[3](0)=6.3096*10^9,psi[1](100)=0,psi[2](100)=0,psi[3](100)=0;

dsolve([ode, ics],numeric);?????????????????????????

Please help me

ode.mws

Hi there!

I want to  plot phase portraits of this fractional system in maple please help me.


                          (alpha_1)
                        ...

Hi,

I want to solve this  fractional differential system in maple please help me.

 


                          (alpha)
                         D        y[0](x) = 0

Hi,

I want to solve this differential inequation in maple please help me.

 

diff(N(t),t)-mu*N(t)<=Pi;

1 2 Page 2 of 2