Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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18 views

Decouple 3 simultaneous 2nd order ODEs (of 3 dependent variables)

I have three simultaneous ODEs with coupled dependent variables. I was wondering whether there's a way for Mathematica to decouple these equations (into three ODEs of a single dependent variable ...
0
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0answers
5 views

Coupled partial diffential equation, with boundaries specification [migrated]

Please, help me to find a books or samples to learn how to solve such coupled equations $$\frac{\partial T_1(x,t)}{\partial t}&= \alpha_1 \frac{\partial^2 T_1(x,t)}{ \partial x^2} +f(x) ...
0
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0answers
68 views

How to solve the heat flow PDE for the constant source term

I have the two dimensional heat flow equation solved for a two dimensional reagion over time. That is an instance I found in the internet. What I am looking for is a method how to determine the heat ...
0
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2answers
111 views

How to solve this equation with NDSolve?

Here is the code: ...
0
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0answers
48 views

Piecewise NDSolveValue: Nested Variable Iteration

I am attempting to make the variable Rc a piecewise-function of [z] and have it update as NDsolve iterates through the range of 'z' such as {z,0,Le), but to no avail. The following code is an attempt ...
2
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1answer
61 views

Simplifying the result of DSolve

I have a system of differential equations that can be solved with DSolve. However, the coefficients are very long there are like terms which can be combined. I used //FullSimplify in my code but the ...
0
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1answer
30 views

Using NDSolve initial conditions as parameters for a function and then a replacement rule

I am trying to make a function based on two initial conditions of a set of differential equations: ...
6
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1answer
85 views

“ParametricSensitivity” in ParametricNDSolve

"ParametricSensitivity" is listed as a Method in the documentation for ParametricNDSolve, ...
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0answers
34 views

How to plot multiple numeric ODE solutions in phase space

I have a system of four coupled ODEs whose solution (and solution process) are sensitive to the value of a parameter $a$. $$\bar X '(t)=\bar F(\bar X, t, a)$$ If possible, I would like to create a ...
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0answers
38 views

Error with ND Solve

I am new to Mathematica, and I am having some issues solving a homework problem of a differential equation. Here is the code: ...
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0answers
76 views

Calculating 15 coupled differential equations

I have 15 coupled differential equations linear in time that need to be solved. Rewriting the equations in a matrix form, they can be expressed following as a single equation, $\frac{d ...
-2
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0answers
37 views

How to assign values to constants inserted in a solution by DSolve

I am trying to solve first order ODE with DSolve, but it didn't pan out. How can I solve for the inserted variable K[1]? Your ...
1
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0answers
46 views

Solving an ODE using shooting method [duplicate]

I have been trying to solve the following nonlinear ordinary differential equation: $$-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0$$ with boundary conditions ...
2
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0answers
32 views

Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
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0answers
42 views
-1
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1answer
116 views

Problem with NDSolve and If

If T=T1, program can calculate. But, when T = T1*If[Abs[q2[t] - q2d] < e1 && Abs[q2'[t]] < e1, 0, 1], program can ...
0
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1answer
60 views

DSolve Error 3D Navier Stokes (z,r,t)

I am essentially wanting to solve Navier Stokes in the [z,r,t] dimensions (2D+Unsteady Flow) for pressure driven flow. However, I keep getting an error I am unable to resolve in my Dsolve such as: ...
1
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1answer
92 views

ODE of an eccentric circle

How can we simplify the solution in: DSolve[ {Sqrt[ 1 - (r[t] - T^2/r[t])^2/(2 a)^2]/(r[t] - T^2/r[t])/(2 a) == r'[t]/ r[t], r[0] == T}, r, t] (r,t) are polar ...
1
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2answers
62 views

Condition on Inside of Region

How do I handle boundary conditions present in the region. Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this ...
0
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1answer
92 views

Nonlinear differential equation: numerical solution

I have to find and plot a numerical solution for this second order differential equation: u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0 where 0 <= x ...
1
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1answer
55 views

How do I restrict the range of an interpolating function in NDSolve?

I have a numerical solution for a differential equation. I know that the gray dotted solution is unphysical. Is there a way I can tell mathematica to ignore the gray dotted solution (e.g. restrict the ...
0
votes
1answer
68 views

How to solve time dependent coupled differential equations? [closed]

I am trying to solve time dependent coupled differential equations with know initial conditions. I am just a beginner in terms of coding so would really appreciate if someone can give me an example of ...
1
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1answer
42 views

Getting the message NDSolve::underdet:

I am solving the wave equation with initial position and velocity function: ...
0
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1answer
59 views

NDSolve does not satisfy initial conditions

For the problem I'm facing, I have three coupled diff eqns that I'm trying to solve ...
0
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2answers
81 views

How to solve a pair of coupled 2nd order equations using shooting method

I have a pair of equations for x[t] and y[t]. Both are 2nd order and they are coupled. Now say that I know the following ...
0
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0answers
33 views

Boundary condition [duplicate]

I'm having the following issue that can not find a solution , by using this boundary condition v[0, t] == u[1, t] that Mathematica does not understand, someone ...
0
votes
1answer
80 views

Improving NDSolve computation speed for 3D stationary PDE

Continuing my last question, I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). The analytical solution for this equation is ...
2
votes
1answer
100 views

Equal flow boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition v[0, t] == u[1, t] that Mathematica does not understand, someone ...
7
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2answers
116 views

Extending NDSolve beyond a singularity

The $\tan$ function satisfies the following IVP: $$y'=1+y^2 ,\quad y(0)=0 $$ and has simple poles at the points $x=\pi/2+ \pi n$ for integer $n$. When trying to get $\tan$ via numerical ...
0
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2answers
96 views

Convert DE to first order?

I have the following set of second-order differential equations: ...
4
votes
4answers
191 views

How should I deal with messages being produced by my Manipulate?

I have made a knockoff of John Polking's dfield for a web-embedded CDF (via Enterprise Mathematica). My code extends that from Belisarius who last year showed me how to use ...
0
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1answer
56 views

Problems with solving two coupled lorenz equation with NDsolve

I have a system of two coupled lorenz equations and I'm to integrate it: ...
1
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0answers
34 views

NDSolve error with a given system of equation [closed]

I know that my question will be very similar to NDSolve giving NDSolve::deqn: message when given my system of equations . Sorry for that, I am so new on Mathematica. I have tried to use the ...
0
votes
1answer
99 views

How to speed up NonlinearModelFit applied on a NDSolve solution?

I'm trying to perform fittings of a model defined through a system of ODEs to data consisting of time courses of a measured quantity. As described in a previous question, the system of ODEs is as ...
0
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0answers
55 views

NDSolve fixed step problem

Working example here: Drive folder (have both files in the same directory! Notice: the line <<variables' in the file seems to throw an error for me, but ...
3
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1answer
47 views

DSolve: Why does Mathematica does a separate integration from 0 instead of 1 and then from 1 to upper limit?

I am trying DSolve in Mathematica for an ODE. Here is the command I am trying and the result I get DSolve[{x'[t] + y[t] x[t] == 0, x[0] == x0}, x[t], t] $$ ...
5
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1answer
125 views

List of unknowns in a differential equation

I often find myself wanting to see what variables/constants are undefined in a large set of differential equations, is there a function that will do this for me? As an example, for the following ODE ...
2
votes
1answer
79 views

Fails to apply NonlinearModelFit on a numerically evaluated model defined as a system of ODEs

I call for your help with because I'm getting troubles to fit a model defined through a system of ODEs. The system of ODEs is as follows: ...
1
vote
1answer
44 views

solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...
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0answers
64 views

Solving a system of first order differential equation with DSolve

How to solve this system of differential equations analytically using Mathematica (using DSolve) $$x'(t)=\frac{a+s}{(1-t)d}x(t)-\frac{b}{(1-t)d}y(t)$$ and ...
4
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2answers
246 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
1
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1answer
30 views

Reverse order in evaluated list

I solve the following set of ODE and plot solution of S1 vs k2 (Figure 1). ...
6
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1answer
94 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
3
votes
2answers
110 views

FEM Solution desired for “Plate with orifice” deflection: Application of Boundary Conditions and use of Regions

I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
11
votes
2answers
122 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
2
votes
1answer
68 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
2
votes
1answer
123 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see ...
8
votes
1answer
179 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ ...
2
votes
0answers
40 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...