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

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2
votes
1answer
78 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
0
votes
1answer
20 views

Plotting a solution of DSolve

I am trying to plot a solution of a differential equation system. This is what I have: ...
0
votes
0answers
15 views

Solving a little heavy differential equation system

I am having some trouble with solving a somewhat heavy differential equation system, which is consisted of 10 variables and other abstract parameters as follows: ...
0
votes
0answers
26 views

Finding derivatives in a differential equation system

I have a differential equation system with 10 variables whose functional forms are: $\lambda_R = \alpha_0 + \alpha_1 P_R$ $E_R = \theta_0 + \theta_1 P_R$ $\lambda_X = \beta_0 + \beta_1 P_X$ $L_D = ...
1
vote
1answer
38 views

Code for time derivative or time differential equation

I have three variables $X, Y, Z$ whose functional form is the following (I also have a function for $Z$ which is somewhat complicated but is not essential for my question here; so it is omitted.): ...
0
votes
0answers
22 views

WhenEvent: forcing the solution to be non-negative for a system of coupled PDEs

I am newbie in Mathematica, but need to use and modify a code written by another person. The code is solving a system of coupled PDEs (reaction-diffusion system) using ...
1
vote
1answer
56 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
1answer
200 views

Indexing of Large Autonomous System of Equations for Use in NDSolve

I currently have a list of ~150 autonomous ODE's that I need to be able to work with using NDSolve. Fortunately I already have them formatted in plaintext, which ...
0
votes
1answer
80 views

Getting message DSolve::conarg:

I want to solve a simple linear PDE about $p_0$ which is a function of ξ, ζ and τ. However, the boundary condition is defined at ζ = h, which is a function of ξ and ...
0
votes
0answers
30 views

NDSolve with mixed boundary conditions

I am trying to solve a spherical Laplace equation subjected to Neumann boundary conditions in the lower half ($θ < π/2$) and constant potential in the other half (say, $f(R,\, θ) = 0,\, {\rm if}\ θ ...
1
vote
1answer
94 views

Smoothing a single rectangular pulse in NDSolve

Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin. I am looking for a smooth function that looks almost exactly the same as the square wave ...
2
votes
4answers
166 views

Output is Input for a Differential with Sign?

Here's the problem: For one of my classes, we're supposed to use Mathematica to solve the equation y''=y-b*y' for a variety of b values and specified boundary conditions and plot the outputs. There I ...
3
votes
0answers
46 views

Increasing MaxPoints in NDSolve results in memory issue

I am interested in increasing "MaxPoints" in NDSolve's "MethodOfLines" in attempt to increase the resolution of the plot of the solution of linearly damped wave equation with transparent boundary ...
0
votes
1answer
116 views

Specifying initial conditions for a PDE

I have simple diffusion equation with point source at c(0, t) = 1 and initial condition c(elsewhere, 0) = 0. How should I apply ...
1
vote
0answers
62 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
0
votes
0answers
53 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
0
votes
1answer
60 views

Substitution of a function in a differential equation

Suppose we have a differential equation as follows: g[t_] := t/2 m[t_] := t/3 A[t_] := {{g[t], 1}, {1, m[t]}} p'[t] == A[t]. p[t], p[0] == {1, 0} ...
0
votes
0answers
54 views

How to find equations of motion and plots? [closed]

I'm doing a project where I need to map the motion of pendulum attached to a spring. I have successfully got the Euler-Lagrangian and both motion but I am having trouble solving the differential ...
5
votes
1answer
88 views

NDSolve and Piecewise functions

I want to clarify upfront, This is not a please help me get the answer to my homework question. I know what I need to do I just do not know how to get mathematica to do it. I am working on an ...
1
vote
1answer
82 views

Can I use the values of interpolating points from NDSolve's output? And How?‎

The output of NDSolve is a (list of)InterpolatingFunction(s). In standard output format the ‎elements of interpolation are not ...
1
vote
0answers
20 views

How to update Plot and some output inside NDSolve callback (StepMonitor)

I have the following problem. I am calling NDSolve to solve a system of first order differential equations (nothing fancy), except that the number of equations measures in thousands and the number ...
1
vote
1answer
84 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
2
votes
1answer
51 views

Question about using NDSolve with a matrix equation

I tried to use NDSolve to study a matrix-valued differential backward equation. The following program seems to work: ...
1
vote
0answers
56 views

NDSolve Wave Equation - Triangular Wave Pulse Inital Condition

I am trying to solve a simple damped wave equation with transparent boundary conditions with triangular shaped piecewise function as my initial condition. I understand that there are issues with this ...
2
votes
1answer
68 views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
2
votes
2answers
86 views
0
votes
0answers
44 views

How to remove error at large time in NDSolve

I am kind of amazed by the fact that Mathematica V9 can't solve a linearly damped wave equation at large time t=200 while Mathematica V8 does without giving me a huge deviation. Intuitively, an ...
1
vote
2answers
173 views

Constraining function found by NDSolve to stay positive

I am trying to constrain my variables in NDSolve so that they stay positive for the integration interval. Is is possible to do that? Using Assumptions as in ...
2
votes
1answer
92 views

How to solve time dependent Optical Bloch Equations for a three level system?

I am trying to solve the optical block equations for three level system which are time dependent, which i generated using the "Atomic Density Matrix" package. When i use the command to solve this 9 ...
1
vote
0answers
43 views

How to explain NDSolve that functions must be positive only?

I have a simple system of differential equations to solve but both functions should be positive: x[t] > 0 and y[t] > 0 for all t. I was not able to explain NDSolve this fact so it goes x[t] < 0 ...
1
vote
1answer
217 views

DSolve will not apply assumption `m ∈ Integers`

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
1answer
124 views

How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
2
votes
0answers
60 views

Numerical Solving Problem, PDE

It is not possibel to solve the given equation numerically or analytically with Mathematica. ...
11
votes
2answers
2k views

Solving an ODE in power series

How do I find a series solution to an ODE? I do not mean taking the Taylor series of an exact solution; I want to solve nasty nonlinear differential equations locally via plug and chug. Surely, that ...
2
votes
2answers
136 views

How to get the series coefficient of a function defined by a differential equation [duplicate]

I need a Taylor series approximation for $x(t)$, which is defined by the following differential equation. $\frac{dx}{dt}=-k_1 x+(1-x)k_2 e^{-k_3 t}$, $x(0)=0$ ...
3
votes
1answer
200 views

Second order differential equation

Hey guys I need someone to give me a hand on this. I don't know if this is too complicated or it's just the lack of knowledge I have on Mathematica. I'm trying to solve the following equation but ...
0
votes
1answer
267 views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
2
votes
0answers
88 views

Coupled Nonlinear Differential Equations Problem

I have a big problem solving a set of coupled nonlinear differential equations using NDSolve. Solving the equations by themselves works quite well but if I want ...
8
votes
3answers
174 views

Wrong answer from DSolve?

I was trying to solve the initial value problem $$u'(t) = \sqrt{u(t)} + \frac{1}{n+1}, \, u(0) = 0$$ using DSolve: ...
4
votes
1answer
89 views

Why I can not get the plot when I use NDSolve`ProcessSolutions?

Why I can not get the plot when I use NDSolve`ProcessSolutions? Anyone can give me a clue. Thanks a lot! ...
1
vote
1answer
59 views

Solution of differential equation in terms of incomplete gamma function

I need help in solving equation 15 and 16 either manually or in Mathematica to get the solution in terms of the incomplete gamma function. This is what Mathematica tells me. I can't understand ...
0
votes
0answers
62 views

Solving a system of DAE on mathematica

I am having trouble solving a system of Differential Algebraic equations of mathematica, the solution I get is just zeros although it should give me an answer, here is my code: ...
2
votes
1answer
59 views

How to use initial fixed timestep, then decrease it according to dependent variable, while spatial stepsize is fixed

I am trying to solve an advection equation. I want to force constant spatial step size (x dimension) with the “MethodOfLines” option, whereas I want to use initially fixed time step size 0.01 then ...
1
vote
4answers
1k views

How do I plot x[t] vs. x'[t] (where x[t] and x'[t] are solutions to NDSolve)?

I have a differential equation which I solved using NDSolve. I can easily plot x[t] vs. t, x'[t] vs. t, but.... how do I plot x[t] vs. x'[t]? I tried using the Evaluate function to simplify things, ...
6
votes
2answers
383 views

Only final result from NDSolve

Finally I started to play with differential equations in Mathematica. And I have faced the problem, which seems too me so basic that I'm afraid this question is going to be closed soon. However, ...
-2
votes
1answer
63 views

Trouble to assign solution of differential equation to a function

I have written a function to Solve the following differential equation where the number n (called in my code Nphoton) is a variable. Nevertheless I have troubles to assign the solutions ...
7
votes
1answer
123 views

Simpler code evaluating Dickman's function?

I've read here that Mathematica 10 can Obtain symbolic solutions to delay differential equations. Would that help in numericaly evaluating Dickman's function $\rho(u)$ ? It is a delay differential ...
8
votes
2answers
343 views

Solve Laplace equation using NDSolve

I am new to Mathematica, a friend recommended this software and started using it, in fact download the trial version to know. I recently did a program in C to calculate numerically the solution to ...
1
vote
1answer
57 views

Save output of NDSolve to a file

I am solving following differential equation using Mathematica, ...
3
votes
1answer
133 views

reconstruct a 3D curve from discrete curvature and torsion

I tried to reconstruct a 3D curve with given curvature and torsion. I saw some threads talking about using runge kutta. However, as far as I see that they required curvature and torsion were ...