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

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1
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1answer
150 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 ...
2
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2answers
147 views

Can Mathematica solve this equation with NDSolve?

Here is my code: ...
0
votes
0answers
55 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 ...
4
votes
2answers
174 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 ...
1
vote
2answers
128 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 ...
2
votes
1answer
264 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 ...
2
votes
2answers
152 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
153 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
1answer
170 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 ...
3
votes
1answer
217 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 ...
9
votes
3answers
219 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: ...
1
vote
1answer
107 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
77 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
91 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 ...
4
votes
1answer
103 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! ...
-2
votes
1answer
93 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 ...
11
votes
2answers
983 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
142 views

Save output of NDSolve to a file

I am solving following differential equation using Mathematica, ...
7
votes
1answer
143 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 ...
3
votes
1answer
178 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 ...
24
votes
1answer
624 views

Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
0
votes
0answers
122 views

How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In particular, I am looking at the ...
-1
votes
1answer
114 views

Differential Equations: Solving a second order ODE with DSolve

I have the following equation h''[η] + (2 a'/a) h'[η] + (k)^2 h[η] == 0 2 a'/a = 1.3551 with boundary conditions ...
1
vote
3answers
132 views

When NSolve fails due to a differential situation?

c = 1.1111; y[x_] = x - c Sin[x] NSolve[y[x] == 0, x] The method has procured no result. Successive derivatives were plotted in an attempt to fix the problem. ...
0
votes
1answer
76 views

DSolve not returning “trivial” solutions [duplicate]

When I enter this DSolve[y'[x]^2 + y[x]^2 == 1, y[x], x] the answer I get is ...
1
vote
1answer
128 views

NDSolve fails for certain choices of parameters and solve range

I'm trying to solve a pair of coupled ODEs with NDSolve. I know roughly what the solution should look like (both should give periodic functions, pi/2 out of phase, the amplitude of which damp towards ...
2
votes
1answer
91 views

Numerically solving systems of (first order) linear delay differential equations

I was wondering, how to solve such a system with mathematica? I found the NDsolve function, but in the reference is not mentioned if it is possible to solve a system of equations.
4
votes
2answers
128 views

NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
1
vote
1answer
88 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
8
votes
2answers
443 views

Driven simple harmonic oscillator — amplitude of steady state motion

I am (partly as an exercise to understand Mathematica) trying to model the response of a damped simple harmonic oscillator to a sinusoidal driving force. I can solve the differential equation with ...
4
votes
1answer
319 views

PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
2
votes
1answer
129 views

Real and Imaginary parts of solutions to a complex linear ODE system

Consider a complex linear ODE system $x'=Ax$, where $$A=\left( \begin{matrix} 0&1\\ -2&-i \end{matrix}\right). $$ One can first find the eigenvalues and eigenvectors using ...
0
votes
0answers
109 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} ...
6
votes
1answer
319 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
0
votes
1answer
89 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 ...
13
votes
2answers
907 views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
1
vote
1answer
107 views

When event and “stop integration”

I am using NDSolve, to solve for an equation. At some point, I want it to stop integrating and keep a constant value for the solution from the point it stopped changing. I tried setting the derivative ...
0
votes
0answers
71 views

How to deal with matrices involved in system of SDEs?

This question is in continuation of the the previous posts Solving Stochastic differential equation and Fast Simulations with Compile. What I want to do is numerically solving the epidemic model which ...
0
votes
1answer
134 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
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0answers
46 views

Conditions for proper integrals with DSolve on Mathematica

DSolve[{RCS'[s] == SNPH[s] - Sqrt[R2[s] - RCS[s]^2]/b,SNPH'[s] == RCS[s]/a^2, R2'[s] == 2 RCS[s] SNPH[s], RCS[0] == 0., SNPH[0] == snal, R2[0] == ri2}, {RCS, SNPH, R2}, s ]; Here {a,b,snal,r12} are ...
7
votes
1answer
156 views

Wrong values at the boundary of differential equation solution

I have a second order ordinary differential equation and want to solve it numerically. Although I have specified values at the boundary, Mathematica solution does not match with boundary conditions. ...
0
votes
0answers
65 views

Discontinuous Forcing for a Cancer Model — Issues with v9 NDSolve

I'm new here, so please be gentle with me and hopefully the post is appropriate and not too basic. I am a math teacher and use modeling in my courses. I had working code (in v8 of Mathematica) for a ...
0
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0answers
101 views

How do I set up conditions at infinity?

I having trouble with this equation: $$ -\frac{(2 m \text{U0}) \Psi (\rho ,z) \left(1-e^{-\text{} \left(\frac{z}{d}\right)^2-\left(\frac{2 \rho -(r+R)}{R-r}\right)^2}\right)}{h^2}+\frac{\partial ...
2
votes
0answers
85 views

Error when using EquationTrekker

I just got to know EquationTrakker because I need to do phase graphs for my classes. When I load it ...
5
votes
1answer
114 views

NDSolve solution violates initial conditions

I have the following code: ...
2
votes
0answers
87 views

Two problems with NDSolve when using Method -> Projection

I tried to solve a system first order differential equations together with a constraint equation. I use the Method -> Projection to check if the constraint holds ...
4
votes
4answers
464 views

DSolve not finding solution I expected

Try to solve the following ODE via DSolve $$ \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. $$ The ...
2
votes
3answers
279 views

How can I get the function of a plotted trajectory? [closed]

I solved two ODEs, which are a function of t, numerically. The first ODE is the vertical equation of motion and the second one is the horizontal equation of that ...
2
votes
1answer
93 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
5
votes
2answers
121 views

Customizing display of partial differential equations

I am manipulating partial differential equations symbolically, and would like to get the easily readable form $\rho \frac{\partial v}{\partial t}$, leaving variables implicit. Based on suggestions ...