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

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14 views

DSolve an ITO process

Hey this place is awesome - I just joined and I am 2 for 2. My newest question is I want to solve the following process: $$ dX(t) = \mu dt+\sigma dW(t) \\ X(0) = 0 $$ We know the solution is the ...
-1
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0answers
88 views

DSolve can't solve such a simple equation

This is the code I have written to get the equation of motion for a simple pendulum. ...
0
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1answer
31 views

Lagrangian for Spring-Pendulum

I solved a Spring-Pendulum System with NDSolve. I tried to plot a graph with the interpolated data but always returns a message "An improperly formatted directive with head Symbol was encountered." ...
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0answers
14 views

PDE: Specify Accuracy Goal/StepSize/WorkingPrecision intervalwise

I am using Mathematica 8. I have two ODEs (in time) and a diffusion PDE (in radius and time) which are all coupled to each other. I solve them using Mathematicas NDSolve by adding a degenerate space ...
1
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1answer
21 views

numerical values for the solution of NDEigensystem

I tried to solve Schrödinger equation in 3D box using the NDEigensystem. My code is: ...
0
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0answers
46 views

How to change equation when singularity happens with NDSolve?

I'm using Euler angle with NDSolve to simulate the precession of the symmetric top. But there's a problem when it comes to singularity, so I need to change to ...
0
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0answers
39 views

Solve heat equation with not constant coefficients and Neumann B.C

I am trying to solve heat equation with not constant coefficients and Neumann BC. this is the equations: $$ (k/r)(∂/∂r (r(∂T/∂r))=ρc_p(T) ( ∂T/∂t) $$ initial condition: $$T(t=0)=20$$ boundaries ...
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0answers
13 views
1
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1answer
102 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. ...
0
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2answers
82 views

Stiff second order ODE

I am trying to solve numericaly $f''=f^{3}-f$, exact solution is Tanh(x). Problem is numerical solution fails if i coming closer to tanh plateau. StiffnessSwitching method dont help. ...
1
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0answers
59 views

Power Spectral Density Plotting

I am new to signal processing.I am analyzing the connection between the behavior of the Rossler model and its parameter c. \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ ...
1
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1answer
64 views

Nonlinear Markov chain (numerical simulation)

Suppose you have a linear Markov process, and you can write it as x(t+1) = Ax(t). Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ...
0
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0answers
4 views

Isothermal coordinates [migrated]

Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E∗(du^2+dv^2)$ and where $E>0$ is an harmonic function? I know that this metric is a special kind ...
0
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1answer
56 views

Stopping NDSolve when encountering stiffness

I am solving a differential equation for different initial conditions using ParametricNDSolveValue. I need to look at the value of the solution at some later point, ...
1
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0answers
115 views

Wave equation PDE with changing boundary condition

This is my first post here, normally with mathematica I will solve out the PDE using eigen function expansion or separation of variables and then model the solution in mathematica. However this time I ...
3
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2answers
151 views
0
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0answers
78 views

Error - Differential equation //2

This is a follow-up question, since it relates to the solution of a modified version of the original differential equation discussed here: Differential equation: NDSolve::berr I receive an error ...
2
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0answers
194 views

DSolve versus DSolveValue [closed]

I've just discovered the new command DSolveValue in Mathematica 10. Is this new command now the preferred instead of DSolve? Is ...
1
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0answers
29 views

Speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions

I have a question on speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions. I build the ODE system with NDSolve...
1
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0answers
57 views

Differential equation: NDSolve::berr

I'm trying to solve the following differential equation. I'm able to obtain a solution, and that solution looks more or less as how the theory predict it should be. ...
1
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2answers
41 views

Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

How do I plot an ParametricPlot with the x-axis using an logarithmic scale? Since I need to use an ParametricPlot, I can not use the LogLinPlot[] and I also was not able to find any viable Solution in ...
1
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1answer
67 views

Differential equation involving history integral

I have not found a solution by using google so I hope I can ask this here. I have an issue with a problem I am trying to solve and I was wondering whether what I am doing is not possible with ...
8
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2answers
317 views

Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
0
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1answer
51 views

Solution of Coupled second-order ODEs and plot the diagram

We have two second-order Coupled differential equations as the followings: $$\left\{\begin{array}{lr} \displaystyle \frac{{{d^2}{y_1}}}{{d{x^2}}} = \{ \frac{{\sqrt {\frac{{1 - {\varepsilon ...
2
votes
1answer
66 views

Will the solution NDSolveValue finds outside of the region I give it give me bogus results?

I'm using NDSolveValue to solve Laplace's equation for a relatively simple system. I have two rectangles, separated by a small gap, which I define using RegionDifference: ...
1
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1answer
73 views

Optimization of the solution to an ODE

Apologies if this is obvious -- I'm very new to Mathematica. I'm trying to minimize the solution to an ODE with respect to a variable. The following code generates the solution to the ODE, ...
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0answers
61 views

How to solve and draw the phase portrait of a linear system [closed]

How to solve and draw the phase portrait of this linear system $\frac{dx}{dt}=Ax$ where $A=\begin{bmatrix}{0}&{2}&{0}\\{-2}&{0}&{0}\\{2}&{0}&{0}\end{bmatrix}$
4
votes
1answer
302 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
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0answers
33 views

How to solve nonlinear system of four PDE

DSolve[{D[Subscript[g, 11][u, v, t], t] == -2 [Psi][u, v, t] Subscript[L, 11][u, v, t], D[Subscript[g, 22][u, v, t], t] == -2 [Psi][u, v, t] Subscript[L, 22][u, v, t], D[Subscript[L, ...
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0answers
72 views

problem with “Infinite expression”, using NDsolve

Im trying to solve an heat equation with NDsolve but i have got a Infinite expression error(1/0). this is the code. ...
3
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4answers
414 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
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1answer
64 views

How to solve different PDE defined in different regions coupled through boundary condition

I would like to solve two different partial differential equations each one defined in a different region and in different coordinates. However the equations are coupled through a boundary condition ...
5
votes
1answer
141 views

Transcritical Bifurcation phase portraits

An example equation for a Transcritical Bifurcations is given by: $$\dfrac{dx}{dt} = f(x, r) = r x - x^2$$ In Mathematica, we can define the function as: ...
2
votes
1answer
67 views

Why does NDSolve and NIntegrate not give the same result? [on hold]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
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0answers
50 views

NDSolve returns solution with single point domain

Thanks to helpful comments from Michael E2 and George2079, I was able to focus in on exactly the source of the issue. With some simplification, I can reduce the problem to: ...
1
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1answer
52 views

How can use Table for two functions obtained from NDSolve? [closed]

I have obtained a numerical solution using NDSolve for two functions a(x) and b(x). how do I use Table to make a list of a(x) vs b(x) values. is it simply Table[{a(x),b(x)},{x,0,100}] or should I use ...
1
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2answers
67 views

Plotting the InterpolatingFunction from NDSolve [closed]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
2
votes
2answers
47 views

Difficulty finding roots of an interpolation function from NDSolve

I have been trying to find the point at which one of the solutions of a system of two ODEs crosses zero. I used the method suggested in this answer to a previous question, which seemed to be the most ...
5
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1answer
133 views

How to use NDSolve with moving boundary conditions?

So I am trying to solve the movement in space and time of a spreading gravity current. The interface satisfies the following PDE: $ \frac{\partial h}{\partial t} = \frac{\partial}{\partial ...
1
vote
1answer
66 views

NDSolve a system of PDE's when one variable does not have an explicit time derivative

Say I want to solve the following set of PDE's (my actual equations are way more complicated, this is just a simplified example to show the structure): $$\begin{align} \partial_t ...
1
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1answer
77 views

Parametric Plot from ODE using WhenEvent

I am searching for a while now, but I don't seem to be able to find an Answer for my Problem - if I am just not able to search properly, I am really sorry. I Simplified my Problem to the following ...
2
votes
0answers
44 views

Solution of the Lagrange's minimal surface equation [closed]

Can I use Mathematica to solve the Lagrange's partial differential equation? $$(1+f_y^2)f_{xx}-2f_xf_yf_{xy}+(1+f_x^2)f_{yy}=0$$ I tried: ...
0
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0answers
40 views

How to handle a special Neumann-like boundary condition in this coupled 2 order differential equations?

How can I solve this problem using Mathematica? I have typed like this(s=0.25δ^4) ...
1
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1answer
87 views

Discontinious Boundary condition NDsolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $U[0,y,t]=0, if, 0<y<1, ...
3
votes
1answer
205 views

NDSolve mixing many scalar and vector equations

I have a set of scalar equations in many unknowns, which I want to combine with a vector equation inside an NDSolve. The equations are a mix of differential and algebraic equations. A set of scalar ...
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0answers
38 views

NDSolve with only discrete variables

Is is possible to use NDSolve with DiscreteVariables if there are no continuous-time variables? This fails: ...
2
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1answer
124 views
0
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0answers
37 views

Solving a 2 dimensional differential with NDSolve, Dirichlet boundary condition

I've tried to solve the following system of equations: \begin{eqnarray} f(x,y)=\lambda^2 \nabla^2 f(x,y)\\ \frac{\partial f}{\partial x}(0,y) =0\\ \frac{\partial f}{\partial y}(0,y) =A\\ ...