Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Hi all,
i'm working with the confluent Heun function (Maple 2019).
Since for the case of an integer coefficient delta or gamma there are two integer Frobenius roots at the regular singularities 0 or 1, there is a logarithmic term in the Frobenius solution at these singularities. So, my question is the following:
When moving around this singularity in the complex plane, the value of the logarithmic term might depend on the choice of the complex logarithm's branch cuts. So, does anybody know just about how HeunC is implemented? Is there sth like a power series solution, which value would in my oppinion depend on this choice of a branch cut?
Or is there another implementation that preserves us from this ambiguity in the case of logarithmic singularities (i.e. integer coefficients in the confluent Heun equation)?

Many thanks,

hello everyone, i have an idea how to implement adomain decomposition method manually but want to transform the whole method on maple for any kind of non-linear ode.

Respected administration I already posted the same question for the other method, pls do not delete my question

 

help_adomian_decomposition_method.mw

Please help to find the exact solution of any ODE by the >sinh or cosh method. I have attached arbitrary ODE here:

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0

 

help.mw

How to solve Linear first-order PDE by the Lagrange method?

dx/(x) =dy/0=dt/0=du/3=dv/v=dw/w, where x,y,t are independent variables and u,v,w are dependent variables.

How to solve the Linear first-order partial differential equation by the Lagrange method. Suppose u and v are dependent variables and x,y,z are independent variables of a partial differential equation of the form:

dx/f(x,y,z)=dy/g(x,y,z)=dz/h(x,y,z)=du/k(x,y,z)=dv/s(x,y,z). I need its solution in the form of u and v . How to find it ?

Can anyone correct me, what's wrong with it.

 

Help_solution.mw

 

 

I have a parametric polynomial which is defined based on the multiplication of different variables and I want to rearrange the polynomial based on specific variables. For example, suppose the polynomial is defined as follows:

a:= (1+x+y)(2x-yx+z)(y^2-zy)

and I want to have a based on first, and second orders of x, or even other variables. Thanks

How can I get Maple to simplify expressions into more meaningful forms?

For example, 

xc1 := -(2*Q*R1 + sqrt(4*Q^2*R1*RL - R1^2 + 2*R1*RL - RL^2))*R1/(4*Q^2*R1 + R1 - RL)

 

The numerator, under the radical, is more meaningful as sqrt(4 Q^2 R1 RL-(R1-RL)^2).

 

Similarly, the denominator can be simplified to Rs(4 Q^2+1)-RL.  

 

How do I get Maple to get me there?

I actually want to numerically solve Karhunen-Loeve Decomposition, which is reduced to homogenous Fredholm integral equation second kind when the kernel is the function of correlation of variables, by using any procedures (Galerkin is better if it is availabe). FYI, with "intsolve" I just got f(x)=0. 

Hi.

in the ThermophysicalData[Chemicals] package that compute the coefficients for different species how I can find that coefficients for seven coefficients not nine of them

in other words, I am seeking to find Databases for the NASA Seven-Coefficient Polynomial Fits for Calculating Thermodynamic Properties of Individual Species.

Best

Hello experts,I need your help to obtain the solution of the mentioned equation in the attached picture by using the newton method by supposing the random value of involved constant like D  etc. I need an algorithm for the newton method for the mentioned equation. note h=1+x^2/2

Hello all

I wanna solve an optimal control problem and I have searched the Internet but I could not find any tutorial or video course on how to solve it with the Pontryagin maximum principle method. It is my first time that I want to use MAPLE for solving an optimal control problem and I would be thankful if someone can help me.

$$\max \int_{0}^{1} x_{2} [u(t)-u(t)^2] dt        $$

$$  \dot{x}_{0} = -(1-u(t)) x_{0}(t)+2 x_{1}(t) $$

$$  \dot{x}_{1}(t) = (1-u_{t}) x_{0}(t) +2 x_{2}(t) -[3-u(t)]x_{1}(t)  $$

$$   \dot{x}_{2}(t) = (1-u(t))x_{1}(t) -2 x_{2}(t)   $$

$$  0 \le u_{t}  \le \frac{1+t^2}{1+t}  $$

 

Thanks

Hi everyone.

I have a 2D function and I wanna after Differentiating from it with respect to tau (at any amount of sigma value) and equaling this derivative to zero solve the infinite system of equations.

P[n](tau)==LegendreP(n - 1/2, cosh(tau)) , Q[n](tau)==LegendreQ(n - 1/2, cosh(tau)) 

are Legendre function.

Thanks in advanced

FUNCTION_f.mw


 

"restart;:N:=3: f(sigma,tau):=(sqrt(cosh(tau)-cos(sigma)))*(∑)(A[n]*P[n]((tau)) -n*Q[n]((tau)) )*sin(n*sigma)"

proc (sigma, tau) options operator, arrow, function_assign; sqrt(cosh(tau)-cos(sigma))*(sum((A[n]*P[n](tau)-n*Q[n](tau))*sin(n*sigma), n = 1 .. N)) end proc

(1)

NULL

W := simplify(diff(f(sigma, tau), tau))

(1/2)*((2*A[2]*(cosh(tau)-cos(sigma))*(diff(P[2](tau), tau))+(-4*cosh(tau)+4*cos(sigma))*(diff(Q[2](tau), tau))+sinh(tau)*(A[2]*P[2](tau)-2*Q[2](tau)))*sin(2*sigma)+(2*A[3]*(cosh(tau)-cos(sigma))*(diff(P[3](tau), tau))+(-6*cosh(tau)+6*cos(sigma))*(diff(Q[3](tau), tau))+sinh(tau)*(A[3]*P[3](tau)-3*Q[3](tau)))*sin(3*sigma)+sin(sigma)*(2*A[1]*(cosh(tau)-cos(sigma))*(diff(P[1](tau), tau))+(-2*cosh(tau)+2*cos(sigma))*(diff(Q[1](tau), tau))+sinh(tau)*(A[1]*P[1](tau)-Q[1](tau))))/(cosh(tau)-cos(sigma))^(1/2)

(2)

``


 

Download FUNCTION_f.mw

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

If I have a tensor T[mu,nu,alpha] in 3-dimensions which is symmetric on {mu,nu} and anti-symmetric on {nu,alpha}, then the number of independent components should be zero. However, if I put this into Maple, using Library:-MinimizeTensorComponents followed by Library:-NumberOfIndependentTensorComponents it returns 4.

Any insight into why it does this would be great, thanks.

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