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

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1answer
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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, ...
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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 ...
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1answer
51 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. ...
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2answers
143 views
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1answer
47 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, ...
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0answers
27 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...
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0answers
75 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 ...
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0answers
55 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. ...
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2answers
36 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 ...
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1answer
64 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 ...
0
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1answer
49 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 ...
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0answers
107 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 ...
1
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1answer
72 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
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
59 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 $A=\begin{bmatrix}{0}&{2}&{0}\\{-2}&{0}&{0}\\{2}&{0}&{0}\end{bmatrix}$
2
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1answer
66 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 ...
5
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1answer
139 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: ...
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2answers
65 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: ...
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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 ...
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2answers
46 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 ...
1
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1answer
62 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 ...
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: ...
3
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0answers
71 views

Solving a matrix differential equation using RBFs

Michael Kelly in the paper http://www.mathematica-journal.com/2010/02/evaluation-of-financial-options-using-radial-basis-functions-in-mathematica/, discussed how to apply Mathematica for solving the ...
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1answer
65 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 ...
2
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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: ...
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1answer
89 views

Sine curve arc length

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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: ...
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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: ...
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1answer
76 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 ...
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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\\ ...
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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) ...
0
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1answer
47 views

Find numerical solution to this system of DE

I am trying to solve this system $$\left( \begin{array}{ccccc} 2 k & -k & 0 & 0 & 0 \\ -k & 2 k & -k & 0 & 0 \\ 0 & -k & 2 k & -k & 0 \\ 0 & 0 ...
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1answer
42 views

How to set MaxStepSize for spatial variable in NDSolve?

When applying NDSolve to a 1-D transient heat equation, the following code appears to set MaxStepSize for the temporal variable t. ...
0
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1answer
49 views

Errors only when code is iterated

Hello I'm trying to have two for loops sweep two parameters and for each 2-tuple of those parameters I want to solve a differential equation. To do this I have the following code: ...
5
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2answers
356 views

How to write a code to solve my ODE problem?

I have the ODE: $$y''+\lambda y = B^3\sin^3(\sqrt{\lambda}x) \ y(0)=0, \int_0^1 y(x)\sin(n\pi x)dx=0$$ I am not sure how to write the mathematica code to solve this ODE, obviously I need here DSolve ...
2
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1answer
123 views

How can I fit cyclic experimental curve with a couple of differential equations?

I have an experimental cyclic curve which looks like this: ...
3
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1answer
71 views
5
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1answer
128 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 ...
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0answers
49 views

What I make wrong with Module command;

I have a differential equations that I have to solve in two parts.e.g: ...
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0answers
54 views

Syntax for Neumann/Robin condition in NDSolve [duplicate]

I can't follow the logic of how a NeumannValue term is to be incorporated into a pde to provide a BC for NDSolve. The ...
3
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1answer
72 views

NDSolve DAE solution order is mixed up

Compare the two solution sets below: in the first one (x == False), there are only 3 dependent variables while in the second one (...
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0answers
44 views

Time dependent/dynamic parameter in the system of ODEs

I am wondering what would be the best way how to code the following situation. I have a solution but I don't think it as elegant as it could be. I have a system with 10 ODEs and lot of parameters. ...
0
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1answer
35 views

Define inverse Laplace operator as map from functions to functions

I am trying to implement the inverse Laplace operator through P[g_] := h /.NDSolve[{h''[x] == g[x], h[0] == 0, h[1] == 0}, h, {x, 0, 1}][[1]] If I now define ...
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0answers
66 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. ...
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2answers
35 views

Beginners problem, Do Loop, Eigenfunction iteration

I am trying to find the first Eigenfunction of the Laplacian (in 1D), i.e. a solution of $$ u''(x)=k u(x)\\ u(0)=u(1)=0 $$ with minimal $k>0$ (in this trivial example, I actually know the analytic ...
2
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1answer
89 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
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26 views

Implementing more accurate boundary conditions in NDSolve

I want to solve a second order differential equation numerically. The boundary conditions are needed to be imposed at z=0 and at ...
1
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1answer
144 views

Plotting Phase Diagram

I have the following problem that I'm sure Mathematica can handle, but it's not working for me! In the following code, I'm trying to replicate the Ramsey Model Phase Diagram. In fact, I want now ...
5
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2answers
272 views

Simpler way to type Derivative[1, 0][u][0, x]

Though not unbearable, I always feel a little nervous when typing partial derivatives at a specified place e.g. $u^{(1,0)}(0,x)$, which happens a lot when setting initial/boundary conditions for PDEs. ...
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0answers
85 views

FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...