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Is it possible to somehow extract a derivative from numeric solution of partial differential equation?

I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.

The actual problem i have is that i have to take a numeric solution, calculate a derivative from it and later use it somewhere else, but the solution that i have is just a set of numbers an array of some sort and i can't really do that because obviously i will get a zero each time.

Perhaps there is a way to interpolate this numeric solution somehow?

I found that someone asked a similar question earlier but i couldn't find an answer for it.

How to solve delay differential equations with Maple?

Example:

diff(x(t),t) = 3*x(t)^2 + 0.3*x(x-0.03)

Hello everyoene, please i have a problem solving this delay differential equation:

y'(x)=cos(x)+y(y(x)-2)    0<x<=10

y(x)=1      x<=0

tau=x-y(x)+2

please i need the solution urgently

http://www.gap-system.org/Manuals/doc/ref/chap50.html

 

which group do four differential electromagnetism belong to in library available in gap system? 

what is the order of the group?

do maple 17 have this group? how to show?

guys ,

in a differential equation i want to expand its variable, but i  have some problem with it for exponential term :jadid.mw

 

 

thanks guys

 

 

How to find the determining equation for a system of fractional differential equation using Maple 15?

How do i proceed to solve two differential equations?

Two equations two unknowns is easy to solve in polynomial algebraic equations. Example: x+y=5; x-y=3; The solution is x=4; y=1 by adding the equations we arrive at.

The two equations are second order differential equations with two variables say temperature T (x,y) and velocity c(x,y). Assume any simple equation (one dimensional as well i.e. T(x) and c(x) which you can demonstrate with ease, I have not formulated the exact equations and boundary conditions yet for SI Engine simulation.

Thanks for comments, suggestions and answers expected eagerly.

Ramakrishnan

Hi,

I am trying to realize the following calculation in Maple.

$
  \left[\sum_{i=0}^n y_i(x) \partial_x^i , \sum_{j=0}^m z_j(x) \partial_x^j \right]  \\
=   \sum_{i=0}^n \sum_{j=0}^m \sum_{l=0}^i  \binom il y_i(x) \left( \partial_x^{i-l} z_j(x)\right) \partial_x^{l+j} \\
- \sum_{j=0}^m \sum_{i=0}^n \sum_{l=0}^j  \binom jl z_j(x) \left( \partial_x^{j-l} z_i(x)\right) \partial_x^{l+i} \ .

$

 

Is there a way to make maple understand d/dx as a differential opperator and calculate with it? When i for example try to calculate diff(d/dx, x) it should give me d^2/dx^2 as a result. Unfortunately i don't know how to realize this.

Basic problem is i don't know how to realize operator expressions in maple like for example:

f(x) d/dx      ( f(x) is a smooth function of x here )

where when applied to a function h(x) it should result in f(x) d/dx h(x) .

 

Is that possible?

 

Thank you very much in advance.

In this section, we will consider several linear dynamical systems in which each mathematical model is a differential equation of second order with constant coefficients with initial conditions specifi ed in a time that we take as t = t0.

All in maple.

 

Vibraciones.mw

(in spanish)

 

Atte.

L.AraujoC.

Hi everybody!

It's nice to join in this forum.

I'm trying to get the analytic solution of the Bernouilli-Euler beam equation, with the next boundary conditions:


w(x,t) = displacements.

w(0,t) = 0   -> It's a cantilever beam. At the x=0 it's clamped.

diff(w(x,t),x) = 0.   -> the gyro in the clamp is zero.

E*I*diff(w(L,t),x,x) = 0  -> the moment at the end of the beam (x=L) is zero.

E*I*diff(w(L,t),x,x,x) = 0  -> the shear at the end of the beam (x=L) is zero too.


I'm not able to introduce the second and the third derivatives as boundary conditions in the pdsolve equation. I post the hole code:

restart;
ode := I*E*(diff(w(x, t), x, x, x, x))+m*(diff(w(x, t), t, t)) = 0;

s := pdsolve(ode, w(x, t));

ode1 := op([2, 1, 1], s);

ode2 := op([2, 1, 2], s);

f1 := op(4, rhs(ode1));

f2 := op(2, rhs(ode2));

sol1 := dsolve(ode1, f1);

sol2 := dsolve(ode2, f2);

sol := rhs(sol1)*rhs(sol2);

conds := [w(0, t) = 0, (D[1](w))(0, t) = 0, eval(I*E*(D[1, 1](w))(x, t), x = L) = 0, eval(I*E*(D[1, 1, 1](w))(x, t), x = L) = 0];

pde := [ode, conds];

pdsolve(pde, w(u, t));


And I get this error:

"Error, (in PDEtools/pdsolve) invalid input: `pdsolve/sys` expects its 1st argument, SYS, to be of type {list({`<>`, `=`, algebraic}), set({`<>`, `=`, algebraic})}, but received [I*E*(diff(diff(diff(diff(w(x, t), x), x), x), x))+m*(diff(diff(w(x, t), t), t)) = 0, [w(0, t) = 0, (D[1](w))(0, t) = 0, I*E*(D[1, 1](w))(L, t) = 0, I*E*(D[1, 1, 1](w))(L, t) = 0]]"


It's seems I'm introducing the Boundary conditions of the second and third derivatives in a wrong way, but I can't discover how to do it.

Thanks very much in advance to everybody!!

Ger89



P.D. - I have use this "tutorial" to write the code ( http://homepages.math.uic.edu/~jan/mcs494f02/Lec34/pde.html ). Thanks very much again. 

 

Hello there, could someone tell me how to input this differential equation?

d2x/dt2 - (3)dx/dt + 2x = 2t -3 

x=2, t=0, dx/dt=4

Hi there,

I'm trying to get the values from the output of a dsolve command.

I have a system of differential equations:

de1 := diff(V(t), t) = V(t)-(1/3)*V(t)^3-W(t)+Ie;
de2 := diff(W(t), t) = 0.8e-1*(V(t)+.7-.8*W(t))

For a range of the independent variable t and for some given values of the parameter Ie, I would like to get the value of the dependent variable V, as well as its minimum/maximum values for each Ie.

Can anybody suggest a solution please?

 

This is the worksheet: MaplePrimes_dsolve_min-max.mw

 

Thanks,

jon

At the internet site of The Heun Project, a strong declaration is made that only Maple incorporates Heun functions, which arise in the solution of differential equations that are extremely important in physics, such as the solution of Schroedinger's equation for the hydrogen atom.  Indeed solutions appear in Heun functions, which are highly obscure and complicated to use because of their five or six arguments, but when one tries to convert them to another function, nothing seems to work.  For instance, if one inquires of FunctionAdvisor(display, HeunG), the resulting list contains

"The location of the "branch cuts" for HeunG are [sic, is] unknown ..." followed by several other "unknown" and an "unable". Such a solution of a differential equation is hollow.

Incidentally, Maple's treatment of integral equations is very weak -- only linear equations with simple solutions, although procedures by David Stoutemyer from 40 years ago are available to enhance this capability.

When can we expect these aspects of Maple to work properly, for applications in physics?

Hi there,

I've got the following differential equation system:,

dU/dt = delta·dotD -lambda·U - kappa·U^2
dL/dt = (1-phi)·lambda·U + 1/4 ·kappa·U^2


being phi, delta, kappa, lambda, kappa some fixed parameters of the system, and where dotD (the derivative wrt time of a function D), which is defined a piecewise funtion:

dotD(t)=1/(3·T1)·DT for t in [0,T1]

dotD(t)=2/(3·(T2-T1-T))·DT for t in [T1+T,T2]

where T and DT are also known, and T1 approaches 0, and T2 approaches T1+T.

Setting the equation system in Maple and trying to solve it, gives a NULL result. However, trying to solve each piece separately seems to work fine.

Why is this?

 

Furthermore, taking limits for the [T1+T,T2] part (having solved each piece separately) yields an invalid limits point error. Ain't the possibility to take limits for both parameters at the same time?

Any ideas?

 

This is the Maple worksheet: MaplePrimes_LQ_model_solve.mw

Thank you.

jon

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #2

This presentation is part of a series of webinars on creating questions in Maple T.A., Maplesoft’s testing and assessment system designed especially for courses involving mathematics. This webinar, which expands on the material offered in Part 1, focuses on using the Question Designer to create many standard types of questions. It will also introduce more advanced question types, such as sketch, free body diagrams, and mathematical formula.

The third and final webinar will wrap up the series with a demonstration of math apps and Maple-graded questions.

To join us for the live presentation, please click here to register.

Clickable Calculus Series – Part #1: Differential Calculus 

In this webinar, Dr. Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Differential Calculus. 

Clickable Calculus™, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

To join us for the live presentation, please click here to register.

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