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

learn more… | top users | synonyms (3)

0
votes
1answer
24 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
votes
1answer
41 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
vote
0answers
104 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 ...
2
votes
2answers
143 views
0
votes
0answers
74 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
votes
0answers
193 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
vote
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...
1
vote
0answers
54 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. ...
0
votes
2answers
34 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
vote
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 ...
8
votes
2answers
314 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
votes
1answer
47 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
vote
1answer
71 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, ...
-4
votes
0answers
59 views

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

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 ...
-2
votes
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, ...
0
votes
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. ...
3
votes
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 ...
3
votes
0answers
69 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 ...
1
vote
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 ...
5
votes
1answer
137 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
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 ...
1
vote
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
vote
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
vote
2answers
62 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
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 ...
5
votes
1answer
127 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
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 ...
1
vote
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 ...
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
votes
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
vote
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 ...
1
vote
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
votes
1answer
123 views
0
votes
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\\ ...
1
vote
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
votes
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 ...
5
votes
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 ...
0
votes
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: ...
10
votes
3answers
4k views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
4
votes
1answer
1k views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
2
votes
1answer
155 views

The numerical solution of a nonlinear ODE: boundary value problem

I want to solve the following nonlinear ordinary differential equation with boundary values $f(0)=1$ and $f(1)=1$: $${\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left( x \right) ={\dfrac { \left( 51-51\,x ...
0
votes
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
votes
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 (...
0
votes
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: ...
0
votes
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. ...