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@Rouben Rostamian  i have two time ...

wolverine 5
July 08 2015
0 0

@Rouben Rostamian  i have two time scales t1 and t2

@Carl Love  d/dt1=D1: and d/dt2+D2 ...

wolverine 5
July 02 2015
0 0

@Carl Love  d/dt1=D1:

and d/dt2+D2

that what i inetend but i think i made some terrible mistake 

i have attached the worksheet .. Thanks ...

wolverine 5
June 30 2015
0 0



> 

restart; with*DEtools(); macro(e = epsilon); eord := 1

e

  

1

 (1)
> 

t := seq(T[j], j = 1 .. eord+1);

T[1], T[2]

 (2)
> 

ode := (D@@2)(y)-epsilon*(1-y^2)*D*y+y = 0;

(D@@2)(y)-epsilon*(1-y^2)*D*y+y = 0

 (3)
> 

ode1 := subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. eord+1), ode);

((D[1]+epsilon*D[2])@@2)(y)-epsilon*(1-y^2)*(D[1]+epsilon*D[2])*y+y = 0

 (4)
> 

y := sum('eta[i]*e^i', 'i' = 0 .. eord);

eta[0]+eta[1]*epsilon

 (5)
> 

ode1 := subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. eord+1), ode);

((D[1]+epsilon*D[2])@@2)(eta[0])+((D[1]+epsilon*D[2])@@2)(eta[1])*epsilon+2*(D[1]+epsilon*D[2])(eta[1])*(D[1]+epsilon*D[2])(epsilon)+eta[1]*((D[1]+epsilon*D[2])@@2)(epsilon)-epsilon*(1-(eta[0]+eta[1]*epsilon)^2)*(D[1]+epsilon*D[2])*(eta[0]+eta[1]*epsilon)+eta[0]+eta[1]*epsilon = 0

 (6)
> 

 

> 

ode2 := simplify(collect(ode1, e), {e^(eord+1) = 0});

2*epsilon(epsilon)*D[2](eta[1])*D[2](epsilon)*epsilon(eta[1])+epsilon(epsilon)*eta[1]*D[2, 2](epsilon)*epsilon(D[1](epsilon)+epsilon(epsilon)*D[2](epsilon))+epsilon(eta[0])*D[1, 2](eta[0])+eta[1]*epsilon(D[1](epsilon)+epsilon(epsilon)*D[2](epsilon))*D[2](epsilon(epsilon))*D[2](epsilon)+epsilon(eta[0])*epsilon(D[1](eta[0])+epsilon(eta[0])*D[2](eta[0]))*D[2, 2](eta[0])+epsilon(D[1](eta[0])+epsilon(eta[0])*D[2](eta[0]))*D[1, 2](eta[0])+epsilon(epsilon)*eta[1]*D[1, 2](epsilon)+2*epsilon(epsilon)*D[1](eta[1])*D[2](epsilon)+epsilon(D[1](eta[0])+epsilon(eta[0])*D[2](eta[0]))*D[2](epsilon(eta[0]))*D[2](eta[0])+eta[1]*D[1](epsilon(epsilon))*D[2](epsilon)+D[1](epsilon(eta[0]))*D[2](eta[0])+eta[1]*epsilon(D[1](epsilon)+epsilon(epsilon)*D[2](epsilon))*D[1, 2](epsilon)+eta[0]+2*D[1](eta[1])*D[1](epsilon)+2*epsilon(eta[1])*D[2](eta[1])*D[1](epsilon)+eta[1]*D[1, 1](epsilon)+D[1, 1](eta[0])+(epsilon(D[1](eta[1])+epsilon(eta[1])*D[2](eta[1]))*D[2](epsilon(eta[1]))*D[2](eta[1])+epsilon(D[1](eta[1])+epsilon(eta[1])*D[2](eta[1]))*D[1, 2](eta[1])-D[1]*eta[0]+D[1, 1](eta[1])+eta[1]+D[1](epsilon(eta[1]))*D[2](eta[1])+epsilon(eta[1])*D[2, 2](eta[1])*epsilon(D[1](eta[1])+epsilon(eta[1])*D[2](eta[1]))+epsilon(eta[1])*D[1, 2](eta[1])+eta[0]^3*D[1])*epsilon = 0

 (7)
> 

 

> 

 

> 

for i to 2 do ODE[i] := coeff(lhs(ode2), e, i) = 0 end do

Error, unable to compute coeff

  
> 

NULL
> 

NULL



Download mltiple_scale_latest.mwmltiple_scale_latest.mw

@Carl Love 

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