MaplePrimes - Questions and Posts tagged with differential
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en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 01 Sep 2015 22:21:02 GMTTue, 01 Sep 2015 22:21:02 GMTThe most recent questions and posts on MaplePrimes tagged with differentialhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with differential
http://www.mapleprimes.com/tags/differential
Skew product does not work properly
http://www.mapleprimes.com/questions/205271-Skew-Product-Does-Not-Work-Properly?ref=Feed:MaplePrimes:Tagged With differential
<p>Good day everyone,</p>
<p> </p>
<p>I want to construct groebner bases over rings of differential Operators.</p>
<p>Thus I used the following:</p>
<p> </p>
<p>with(Ore_algebra);</p>
<p>with(Groebner); N := 3;</p>
<p>A := skew_algebra(diff = [D[1], x[1]], diff = [D[2], x[2]], diff = [D[3], x[3]], comm = i, alg_relations = i^2+1); T := MonomialOrder(A, tdeg(D[1], D[2], D[3]));</p>
<p>A["polynomial_indets"]; [returns {D[1], D[2], D[3]}]</p>
<p>A["rational_indets"]; [returns {i, x[1], x[2], x[3]}]</p>
<p> </p>
<p>So far everything seems as it should be: The ring i wanted to define here is the third Ring of Differential operators over the field of complex 'rational' functions and maple returns that indeed it will handle the D[i] as monomials and the rest as coefficients for them.</p>
<p> </p>
<p>Hover, when i use the Skew product, the following happens:</p>
<p>skew_product(x[1],D[1],A) [returns D[1]x[1]+1}]</p>
<p>skew_product(x[1],D[1],A) [returns D[1]x[1]]<br><br>Both is wrong, but maple seems to 'know' this. It used the correct relation to in the first product, the only thing it didn't do was switch D[1] and x[1]. I think maple handles the result of the skew product as if it was a commutative product and always places the D[i] at the left but still 'knows' what the actual result is.</p>
<p>The actual results should have been x[1]D[1]+1 for the first and x[1]*D[1] for the second product.</p>
<p> </p>
<p>In the second product, it seems like maple treated x[1]*D[1] as if the Elements were switched already.</p>
<p> </p>
<p>What i want though is for maple to correctly display the skew products and return the products so that in every summand the D[i] are at the right side and their coefficients are at the left side (and if possible (i do not know how to do that yet) sort the result of a skew product in a way that displays every different Power product of the D[i] with their coefficients, so that i get (x[1]+x[2])*D[2] and not x[1]*D[2]+x[2]*D[2]).</p>
<p> </p>
<p>Can anyone help me here?</p>
<p> </p>
<p><br> <br> <br> <br> </p><p>Good day everyone,</p>
<p> </p>
<p>I want to construct groebner bases over rings of differential Operators.</p>
<p>Thus I used the following:</p>
<p> </p>
<p>with(Ore_algebra);</p>
<p>with(Groebner); N := 3;</p>
<p>A := skew_algebra(diff = [D[1], x[1]], diff = [D[2], x[2]], diff = [D[3], x[3]], comm = i, alg_relations = i^2+1); T := MonomialOrder(A, tdeg(D[1], D[2], D[3]));</p>
<p>A["polynomial_indets"]; [returns {D[1], D[2], D[3]}]</p>
<p>A["rational_indets"]; [returns {i, x[1], x[2], x[3]}]</p>
<p> </p>
<p>So far everything seems as it should be: The ring i wanted to define here is the third Ring of Differential operators over the field of complex 'rational' functions and maple returns that indeed it will handle the D[i] as monomials and the rest as coefficients for them.</p>
<p> </p>
<p>Hover, when i use the Skew product, the following happens:</p>
<p>skew_product(x[1],D[1],A) [returns D[1]x[1]+1}]</p>
<p>skew_product(x[1],D[1],A) [returns D[1]x[1]]<br><br>Both is wrong, but maple seems to 'know' this. It used the correct relation to in the first product, the only thing it didn't do was switch D[1] and x[1]. I think maple handles the result of the skew product as if it was a commutative product and always places the D[i] at the left but still 'knows' what the actual result is.</p>
<p>The actual results should have been x[1]D[1]+1 for the first and x[1]*D[1] for the second product.</p>
<p> </p>
<p>In the second product, it seems like maple treated x[1]*D[1] as if the Elements were switched already.</p>
<p> </p>
<p>What i want though is for maple to correctly display the skew products and return the products so that in every summand the D[i] are at the right side and their coefficients are at the left side (and if possible (i do not know how to do that yet) sort the result of a skew product in a way that displays every different Power product of the D[i] with their coefficients, so that i get (x[1]+x[2])*D[2] and not x[1]*D[2]+x[2]*D[2]).</p>
<p> </p>
<p>Can anyone help me here?</p>
<p> </p>
<p><br> <br> <br> <br> </p>205271Tue, 01 Sep 2015 04:16:27 ZkoljjakoljjaDerivative from pdsolve/numeric solution?
http://www.mapleprimes.com/questions/204424-Derivative-From-Pdsolvenumeric-Solution?ref=Feed:MaplePrimes:Tagged With differential
<p>Is it possible to somehow extract a derivative from numeric solution of partial differential equation?</p>
<p>I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.</p>
<p>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.</p>
<p>Perhaps there is a way to interpolate this numeric solution somehow?</p>
<p>I found that someone asked a similar question earlier but i couldn't find an answer for it.</p><p>Is it possible to somehow extract a derivative from numeric solution of partial differential equation?</p>
<p>I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.</p>
<p>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.</p>
<p>Perhaps there is a way to interpolate this numeric solution somehow?</p>
<p>I found that someone asked a similar question earlier but i couldn't find an answer for it.</p>204424Sun, 07 Jun 2015 23:28:18 Znorthpole11northpole11How to solve delay differential equations with Maple?
http://www.mapleprimes.com/questions/204421-How-To-Solve-Delay-Differential-Equations?ref=Feed:MaplePrimes:Tagged With differential
<p>How to solve delay differential equations with Maple?</p>
<p>Example:</p>
<p>diff(x(t),t) = 3*x(t)^2 + 0.3*x(x-0.03)</p><p>How to solve delay differential equations with Maple?</p>
<p>Example:</p>
<p>diff(x(t),t) = 3*x(t)^2 + 0.3*x(x-0.03)</p>204421Sat, 06 Jun 2015 16:13:40 ZaskuyueaskuyueDELAY DIFFERENTIAL EQUATIONS
http://www.mapleprimes.com/questions/204395-DELAY-DIFFERENTIAL-EQUATIONS?ref=Feed:MaplePrimes:Tagged With differential
<p>Hello everyoene, please i have a problem solving this delay differential equation:</p>
<p>y'(x)=cos(x)+y(y(x)-2) 0<x<=10</p>
<p>y(x)=1 x<=0</p>
<p>tau=x-y(x)+2</p>
<p>please i need the solution urgently</p><p>Hello everyoene, please i have a problem solving this delay differential equation:</p>
<p>y'(x)=cos(x)+y(y(x)-2) 0<x<=10</p>
<p>y(x)=1 x<=0</p>
<p>tau=x-y(x)+2</p>
<p>please i need the solution urgently</p>204395Wed, 03 Jun 2015 12:54:49 Zyemisiyemisiwhich group do four differential electromagnetism belong to?
http://www.mapleprimes.com/questions/204359-Which-Group-Do-Four-Differential-Electromagnetism?ref=Feed:MaplePrimes:Tagged With differential
<p>http://www.gap-system.org/Manuals/doc/ref/chap50.html</p>
<p> </p>
<p>which group do four differential electromagnetism belong to in library available in gap system? </p>
<p>what is the order of the group?</p>
<p>do maple 17 have this group? how to show?</p><p>http://www.gap-system.org/Manuals/doc/ref/chap50.html</p>
<p> </p>
<p>which group do four differential electromagnetism belong to in library available in gap system? </p>
<p>what is the order of the group?</p>
<p>do maple 17 have this group? how to show?</p>204359Sun, 31 May 2015 13:03:11 Zritritexpansion in a differential equations
http://www.mapleprimes.com/questions/204332-Expansion-In-A-Differential-Equations?ref=Feed:MaplePrimes:Tagged With differential
<p>guys ,</p>
<p>in a differential equation i want to expand its variable, but i have some problem with it for exponential term :<a href="/view.aspx?sf=204332_question/jadid.mw">jadid.mw</a></p>
<p> </p>
<p> </p>
<p>thanks guys</p>
<p> </p>
<p> </p><p>guys ,</p>
<p>in a differential equation i want to expand its variable, but i have some problem with it for exponential term :<a href="/view.aspx?sf=204332_question/jadid.mw">jadid.mw</a></p>
<p> </p>
<p> </p>
<p>thanks guys</p>
<p> </p>
<p> </p>204332Thu, 28 May 2015 16:54:37 ZlhamlhamSolving fractional differential equation
http://www.mapleprimes.com/questions/204226-Solving-Fractional-Differential-Equation?ref=Feed:MaplePrimes:Tagged With differential
<p>How to find the determining equation for a system of fractional differential equation using Maple 15?</p><p>How to find the determining equation for a system of fractional differential equation using Maple 15?</p>204226Thu, 14 May 2015 08:59:11 ZbirabiraSolving two or three simultaneous second order differential equations - Any method avaiable
http://www.mapleprimes.com/questions/203801-Solving-Two-Or-Three-Simultaneous-Second?ref=Feed:MaplePrimes:Tagged With differential
<p>How do i proceed to solve two differential equations?</p>
<p>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.</p>
<p>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.</p>
<p>Thanks for comments, suggestions and answers expected eagerly.</p>
<p>Ramakrishnan</p><p>How do i proceed to solve two differential equations?</p>
<p>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.</p>
<p>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.</p>
<p>Thanks for comments, suggestions and answers expected eagerly.</p>
<p>Ramakrishnan</p>203801Tue, 24 Mar 2015 23:18:03 ZramakrishnanramakrishnanCalculate differential of commutators
http://www.mapleprimes.com/questions/203611-Calculate-Differential-Of-Commutators?ref=Feed:MaplePrimes:Tagged With differential
<p>Hi,</p>
<p>I am trying to realize the following calculation in Maple.</p>
<p>$<br> \left[\sum_{i=0}^n y_i(x) \partial_x^i , \sum_{j=0}^m z_j(x) \partial_x^j \right] \\ <br>= \sum_{i=0}^n \sum_{j=0}^m \sum_{l=0}^i \binom il y_i(x) \left( \partial_x^{i-l} z_j(x)\right) \partial_x^{l+j} \\ <br>- \sum_{j=0}^m \sum_{i=0}^n \sum_{l=0}^j \binom jl z_j(x) \left( \partial_x^{j-l} z_i(x)\right) \partial_x^{l+i} \ .</p>
<p>$</p>
<p> </p>
<p>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.</p>
<p>Basic problem is i don't know how to realize operator expressions in maple like for example:</p>
<p>f(x) d/dx ( f(x) is a smooth function of x here )</p>
<p>where when applied to a function h(x) it should result in f(x) d/dx h(x) .</p>
<p> </p>
<p>Is that possible?</p>
<p> </p>
<p>Thank you very much in advance.</p><p>Hi,</p>
<p>I am trying to realize the following calculation in Maple.</p>
<p>$<br /> \left[\sum_{i=0}^n y_i(x) \partial_x^i , \sum_{j=0}^m z_j(x) \partial_x^j \right] \\ <br />= \sum_{i=0}^n \sum_{j=0}^m \sum_{l=0}^i \binom il y_i(x) \left( \partial_x^{i-l} z_j(x)\right) \partial_x^{l+j} \\ <br />- \sum_{j=0}^m \sum_{i=0}^n \sum_{l=0}^j \binom jl z_j(x) \left( \partial_x^{j-l} z_i(x)\right) \partial_x^{l+i} \ .</p>
<p>$</p>
<p> </p>
<p>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.</p>
<p>Basic problem is i don't know how to realize operator expressions in maple like for example:</p>
<p>f(x) d/dx ( f(x) is a smooth function of x here )</p>
<p>where when applied to a function h(x) it should result in f(x) d/dx h(x) .</p>
<p> </p>
<p>Is that possible?</p>
<p> </p>
<p>Thank you very much in advance.</p>203611Tue, 03 Mar 2015 14:34:44 ZflapjackflapjackVibrations with maple
http://www.mapleprimes.com/posts/200679-Vibrations-With-Maple?ref=Feed:MaplePrimes:Tagged With differential
<p>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.</p>
<p>All in maple.</p>
<p> </p>
<p><a href="/view.aspx?sf=200679_post/Vibraciones.mw">Vibraciones.mw</a></p>
<p>(in spanish)</p>
<p> </p>
<p>Atte.</p>
<p>L.AraujoC.</p><p>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.</p>
<p>All in maple.</p>
<p> </p>
<p><a href="/view.aspx?sf=200679_post/Vibraciones.mw">Vibraciones.mw</a></p>
<p>(in spanish)</p>
<p> </p>
<p>Atte.</p>
<p>L.AraujoC.</p>200679Thu, 26 Feb 2015 17:40:10 ZLenin Araujo CastilloLenin Araujo CastilloIntroducing high order derivatives values in fixed points as boundary conditions in PDSolve.
http://www.mapleprimes.com/questions/203460-Introducing-High-Order-Derivatives-Values?ref=Feed:MaplePrimes:Tagged With differential
<p>Hi everybody!<br><br>It's nice to join in this forum.<br><br>I'm trying to get the analytic solution of the Bernouilli-Euler beam equation, with the next boundary conditions:</p>
<p style="padding-left: 30px;"><br>w(x,t) = displacements.<br><br>w(0,t) = 0 -> It's a cantilever beam. At the x=0 it's clamped.</p>
<p style="padding-left: 30px;">diff(w(x,t),x) = 0. -> the gyro in the clamp is zero.</p>
<p style="padding-left: 30px;">E*I*diff(w(L,t),x,x) = 0 -> the moment at the end of the beam (x=L) is zero.</p>
<p style="padding-left: 30px;">E*I*diff(w(L,t),x,x,x) = 0 -> the shear at the end of the beam (x=L) is zero too.</p>
<p><br>I'm not able to introduce the second and the third derivatives as boundary conditions in the pdsolve equation. I post the hole code:</p>
<p style="padding-left: 30px;">restart; <br>ode := I*E*(diff(w(x, t), x, x, x, x))+m*(diff(w(x, t), t, t)) = 0;</p>
<p style="padding-left: 30px;">s := pdsolve(ode, w(x, t));</p>
<p style="padding-left: 30px;">ode1 := op([2, 1, 1], s);</p>
<p style="padding-left: 30px;">ode2 := op([2, 1, 2], s);</p>
<p style="padding-left: 30px;">f1 := op(4, rhs(ode1));</p>
<p style="padding-left: 30px;">f2 := op(2, rhs(ode2));</p>
<p style="padding-left: 30px;">sol1 := dsolve(ode1, f1);</p>
<p style="padding-left: 30px;">sol2 := dsolve(ode2, f2);</p>
<p style="padding-left: 30px;">sol := rhs(sol1)*rhs(sol2);</p>
<p style="padding-left: 30px;">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];</p>
<p style="padding-left: 30px;">pde := [ode, conds];</p>
<p style="padding-left: 30px;">pdsolve(pde, w(u, t));</p>
<p><br>And I get this error:<br><br>"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]]"</p>
<p><br>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.<br><br>Thanks very much in advance to everybody!!<br><br></p>
<p>Ger89</p>
<p><br><br>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. </p>
<p> </p><p>Hi everybody!<br /><br />It's nice to join in this forum.<br /><br />I'm trying to get the analytic solution of the Bernouilli-Euler beam equation, with the next boundary conditions:</p>
<p style="padding-left: 30px;"><br />w(x,t) = displacements.<br /><br />w(0,t) = 0 -> It's a cantilever beam. At the x=0 it's clamped.</p>
<p style="padding-left: 30px;">diff(w(x,t),x) = 0. -> the gyro in the clamp is zero.</p>
<p style="padding-left: 30px;">E*I*diff(w(L,t),x,x) = 0 -> the moment at the end of the beam (x=L) is zero.</p>
<p style="padding-left: 30px;">E*I*diff(w(L,t),x,x,x) = 0 -> the shear at the end of the beam (x=L) is zero too.</p>
<p><br />I'm not able to introduce the second and the third derivatives as boundary conditions in the pdsolve equation. I post the hole code:</p>
<p style="padding-left: 30px;">restart; <br />ode := I*E*(diff(w(x, t), x, x, x, x))+m*(diff(w(x, t), t, t)) = 0;</p>
<p style="padding-left: 30px;">s := pdsolve(ode, w(x, t));</p>
<p style="padding-left: 30px;">ode1 := op([2, 1, 1], s);</p>
<p style="padding-left: 30px;">ode2 := op([2, 1, 2], s);</p>
<p style="padding-left: 30px;">f1 := op(4, rhs(ode1));</p>
<p style="padding-left: 30px;">f2 := op(2, rhs(ode2));</p>
<p style="padding-left: 30px;">sol1 := dsolve(ode1, f1);</p>
<p style="padding-left: 30px;">sol2 := dsolve(ode2, f2);</p>
<p style="padding-left: 30px;">sol := rhs(sol1)*rhs(sol2);</p>
<p style="padding-left: 30px;">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];</p>
<p style="padding-left: 30px;">pde := [ode, conds];</p>
<p style="padding-left: 30px;">pdsolve(pde, w(u, t));</p>
<p><br />And I get this error:<br /><br />"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]]"</p>
<p><br />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.<br /><br />Thanks very much in advance to everybody!!<br /><br /></p>
<p>Ger89</p>
<p><br /><br />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. </p>
<p> </p>203460Tue, 10 Feb 2015 17:46:55 Zger89ger89how to input 2nd order differential equation?
http://www.mapleprimes.com/questions/203442-How-To-Input-2nd-Order-Differential-Equation?ref=Feed:MaplePrimes:Tagged With differential
<p>Hello there, could someone tell me how to input this differential equation?</p>
<p>d<sup>2</sup>x/dt<sup>2</sup> - (3)dx/dt + 2x = 2t -3 <sup><br></sup></p>
<p>x=2, t=0, dx/dt=4</p><p>Hello there, could someone tell me how to input this differential equation?</p>
<p>d<sup>2</sup>x/dt<sup>2</sup> - (3)dx/dt + 2x = 2t -3 <sup><br /></sup></p>
<p>x=2, t=0, dx/dt=4</p>203442Sun, 08 Feb 2015 10:28:47 ZUndergradMathsUndergradMathsGet values from numerical solving
http://www.mapleprimes.com/questions/203436-Get-Values-From-Numerical-Solving?ref=Feed:MaplePrimes:Tagged With differential
<p>Hi there,</p>
<p>I'm trying to get the values from the output of a dsolve command.</p>
<p>I have a system of differential equations:</p>
<p><strong><em>de1 := diff(V(t), t) = V(t)-(1/3)*V(t)^3-W(t)+Ie; </em></strong><br><strong><em>de2 := diff(W(t), t) = 0.8e-1*(V(t)+.7-.8*W(t))</em></strong></p>
<p>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.</p>
<p>Can anybody suggest a solution please?</p>
<p> </p>
<p>This is the worksheet: <a href="/view.aspx?sf=203436_question/MaplePrimes_dsolve_min-max.mw">MaplePrimes_dsolve_min-max.mw</a></p>
<p> </p>
<p>Thanks,</p>
<p>jon</p><p>Hi there,</p>
<p>I'm trying to get the values from the output of a dsolve command.</p>
<p>I have a system of differential equations:</p>
<p><strong><em>de1 := diff(V(t), t) = V(t)-(1/3)*V(t)^3-W(t)+Ie; </em></strong><br><strong><em>de2 := diff(W(t), t) = 0.8e-1*(V(t)+.7-.8*W(t))</em></strong></p>
<p>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.</p>
<p>Can anybody suggest a solution please?</p>
<p> </p>
<p>This is the worksheet: <a href="/view.aspx?sf=203436_question/MaplePrimes_dsolve_min-max.mw">MaplePrimes_dsolve_min-max.mw</a></p>
<p> </p>
<p>Thanks,</p>
<p>jon</p>203436Sat, 07 Feb 2015 17:35:56 ZjonlgjonlgHeun functions in Maple
http://www.mapleprimes.com/questions/203384-Heun-Functions-In-Maple?ref=Feed:MaplePrimes:Tagged With differential
<p>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</p>
<p>"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.</p>
<p>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.</p>
<p>When can we expect these aspects of Maple to work properly, for applications in physics?</p><p>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</p>
<p>"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.</p>
<p>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.</p>
<p>When can we expect these aspects of Maple to work properly, for applications in physics?</p>203384Sat, 31 Jan 2015 21:35:12 ZJ F OgilvieJ F OgilvieSolving a piecewise differential equation system
http://www.mapleprimes.com/questions/203283-Solving-A-Piecewise-Differential-Equation-System?ref=Feed:MaplePrimes:Tagged With differential
<p>Hi there,</p>
<p>I've got the following differential equation system:,</p>
<p><em>dU/dt = delta·dotD -lambda·U - kappa·U^2</em><br><em>dL/dt = (1-phi)·lambda·U + 1/4 ·kappa·U^2</em></p>
<p><br>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:</p>
<p><em>dotD(t)=1/(3·T1)·DT for t in [0,T1]</em></p>
<p><em>dotD(t)=2/(3·(T2-T1-T))·DT for t in [T1+T,T2]</em></p>
<p>where T and DT are also known, and T1 approaches 0, and T2 approaches T1+T.</p>
<p><strong>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.</strong></p>
<p><strong>Why is this?</strong></p>
<p> </p>
<p>Furthermore, <strong>taking limits for the [T1+T,T2] part (having solved each piece separately) yields </strong>an invalid limits point<strong> error. Ain't the possibility to take limits for both parameters at the same time?</strong></p>
<p>Any ideas?</p>
<p> </p>
<p>This is the Maple worksheet: <a href="/view.aspx?sf=203283_question/MaplePrimes_LQ_model_solve.mw">MaplePrimes_LQ_model_solve.mw</a></p>
<p>Thank you.</p>
<p>jon</p><p>Hi there,</p>
<p>I've got the following differential equation system:,</p>
<p><em>dU/dt = delta·dotD -lambda·U - kappa·U^2</em><br><em>dL/dt = (1-phi)·lambda·U + 1/4 ·kappa·U^2</em></p>
<p><br>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:</p>
<p><em>dotD(t)=1/(3·T1)·DT for t in [0,T1]</em></p>
<p><em>dotD(t)=2/(3·(T2-T1-T))·DT for t in [T1+T,T2]</em></p>
<p>where T and DT are also known, and T1 approaches 0, and T2 approaches T1+T.</p>
<p><strong>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.</strong></p>
<p><strong>Why is this?</strong></p>
<p> </p>
<p>Furthermore, <strong>taking limits for the [T1+T,T2] part (having solved each piece separately) yields </strong>an invalid limits point<strong> error. Ain't the possibility to take limits for both parameters at the same time?</strong></p>
<p>Any ideas?</p>
<p> </p>
<p>This is the Maple worksheet: <a href="/view.aspx?sf=203283_question/MaplePrimes_LQ_model_solve.mw">MaplePrimes_LQ_model_solve.mw</a></p>
<p>Thank you.</p>
<p>jon</p>203283Fri, 16 Jan 2015 19:23:31 Zjonlgjonlg