mskalsi

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8 years, 214 days

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These are questions asked by mskalsi

Dear All

Please see my query below:


 

Suppose I have a expression whose terms are in summation:

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)

(1)

diff(sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity), xi)

sum(P[n]*xi^n*n/xi, n = 0 .. infinity)+2*(sum(P[n]*xi^n, n = 0 .. infinity))*(sum(P[n]*xi^n*n/xi, n = 0 .. infinity))+sum(P[2*n+1]*P[2*n]*xi^n*n/xi, n = 0 .. infinity)

(2)

In above summation, how I can write specific term ? For example, how I can display term for n = 2etc.

NULL


 

Download Summation.mw

Dear all

I am trying to solve system of ODEs by TWS command for traveling wave solution, but an error is showing. When I enter sinlge ODE or PDE the command does not show any error. Why it is showing error for system of ODEs ?


 

with(PDEtools, TWSolutions, declare):

with(DEtools):

Sys := {125*xi^3*(diff(f(xi), xi, xi, xi))-90*f(xi)*xi*(diff(h(xi), xi))-180*h(xi)*xi*(diff(f(xi), xi))+750*xi^2*(diff(f(xi), xi, xi))-180*f(xi)*h(xi)+830*xi*(diff(f(xi), xi))+80*f(xi)-108*(diff(h(xi), xi)), 15*f(xi)*xi*(diff(f(xi), xi))+6*f(xi)^2+10*xi*(diff(g(xi), xi))+8*g(xi)+6*(diff(f(xi), xi)) = 0, 5*f(xi)*xi*(diff(g(xi), xi))+10*g(xi)*xi*(diff(f(xi), xi))+8*f(xi)*g(xi)+10*xi*(diff(h(xi), xi))+12*h(xi)+6*(diff(g(xi), xi)) = 0}

TWSolutions(Sys)

Error, (in pdsolve/sys/info) required an indication of the solving variables for the given system

 

``


 

Download ODEs.mw

Dear All

I am stucked at converting an differential expression in Jet notations. Maple is giving error as  expression contains composite derivatives. Please see attached file.


 

with(PDEtools, D_Dx, declare, ToJet, FromJet):

DepVars := [alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

[alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

(1)

alias(alpha = alpha(x, y, t), beta = beta(x, y, t), xi = xi(x, y, t), tau = tau(x, y, t), eta = eta(x, y, t), U = U(xi(x, y, t), tau(x, y, t), eta(x, y, t)))

alpha, beta, xi, tau, eta, U

(2)

declare(alpha, beta, xi, tau, eta, U)

alpha(x, y, t)*`will now be displayed as`*alpha

 

beta(x, y, t)*`will now be displayed as`*beta

 

xi(x, y, t)*`will now be displayed as`*xi

 

tau(x, y, t)*`will now be displayed as`*tau

 

eta(x, y, t)*`will now be displayed as`*eta

 

U(xi(x, y, t), tau(x, y, t), eta(x, y, t))*`will now be displayed as`*U

(3)

u := U*beta+alpha

beta*U+alpha

(4)

diff(u, x)

(diff(beta, x))*U+beta*((D[1](U))(xi, tau, eta)*(diff(xi, x))+(D[2](U))(xi, tau, eta)*(diff(tau, x))+(D[3](U))(xi, tau, eta)*(diff(eta, x)))+diff(alpha, x)

(5)

ToJet((diff(beta, x))*U+beta*((D[1](U))(xi, tau, eta)*(diff(xi, x))+(D[2](U))(xi, tau, eta)*(diff(tau, x))+(D[3](U))(xi, tau, eta)*(diff(eta, x)))+diff(alpha, x), DepVars)

Error, invalid input: PDEtools:-ToJet expects its 2nd argument, DepVars, to be of type Or(`PDEtools/F(...)`, name, And(Or(list({name, `PDEtools/F(...)`}), set({name, `PDEtools/F(...)`})), satisfies(proc (SL) options operator, arrow; evalb(0 < nops(SL)) end proc))), but received [alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

 

I guess ToJet is not working in case of composite function.

But how I can  display derivatived (D[1](U))(xi, tau, eta)as U[xi]


 

Download Composite_Derivative.mw

Dear All

For six parameters, I have corresponding list of their values and there are eight values for every parameter. I need to put these values in a formula to obtain a list of output values. There are two formulas one for 'P' and next is for 'RL'. I have used value of 'P' to calculate value of 'RL'. There are some complex number too, for which I have used modulus and final value is calculated by using 'evalf', but this command is not returning proper values for list as required. But this command works fine when I use single value from every list to calculate RL.

The Maple sheet attached herewith.

List.mw

Regards

From differential expression I am trying to extract coefficients corresponding to given indets, but the coeffs command is giving me error as "invalid argument to coeffs"

For example for worksheet titled "[852] Determining Equations using Prolongation" the error is showing for expression (9).

Whereas the same command in worksheet titled "[411] Determining Equations for Variable Coeff KdV(Reviewed)" is working okay and is giving desired result at (16).

I am running both worksheets in Maple 18.

 

[852]_Determining_Equations_Using_Prolongation.mw

[411]_Determing_Equations_for_Variable_coefficient_KdV_(reviewed).mw

Regards

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