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

learn more… | top users | synonyms

2
votes
1answer
65 views

Driven SHO - amplitude of steady state motion

I am (partly as an exercise to understand Mathematica) trying to model the response of a damped SHO to a sinusoidal driving force. I can solve the differential equation with some arbitrarily chosen ...
0
votes
0answers
32 views

Solving system of 9 differential equations with Im & Re parts

I tried to solve a system of nine differential equations. Actually, I tried to do it in two ways, and both of them give me the same error: NDSolve::pdord: Some of the functions have zero ...
3
votes
1answer
81 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 ...
1
vote
1answer
55 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
1answer
54 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 ...
-1
votes
0answers
62 views

Dsolve implicit solution to a Differential Equation [on hold]

I would like to know if there is a form that Mathematica can give me the implicit solution to an ODE. When I use Mathematica of Alpha it it always seem to solve it for y (the dependent variable) but ...
0
votes
0answers
56 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} ...
5
votes
1answer
202 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: ...
10
votes
1answer
163 views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
0
votes
0answers
40 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
0answers
24 views

What are the upper bound and stability conditions for the following simple linear system [migrated]

Consider the following linear system $$\dot{x}=\sum\limits_{i=1}^{m}{{{\alpha }_{i}}}\left( t \right)\cdot {{A}_{i}}\cdot x \quad (1) $$ where, $x\in {{\mathbb{R}}^{n}}$ represents the state vector, ...
4
votes
3answers
267 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 ...
1
vote
1answer
46 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
1answer
88 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
27 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 ...
6
votes
1answer
143 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. ...
6
votes
2answers
4k views

Integral equation numerical solution with NDSolve

I'm trying to solve something like: f[x] == Integrate[f[x]*g[x]] where g[x] is known and ...
0
votes
0answers
54 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 ...
5
votes
2answers
85 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 ...
0
votes
0answers
89 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 ...
0
votes
2answers
81 views

Higher order eigenvalue problem [closed]

Does anybody know some ideas, references or something like these to solve such third order eigenvalue problem using Mathematica: $\Psi'''(x) + (1 - 4x^2) \Psi'(x) - 6x\Psi(x) = E \Psi(x)$
2
votes
0answers
51 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
94 views
2
votes
0answers
39 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 ...
2
votes
3answers
206 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
88 views
0
votes
0answers
38 views

NDSolve::derarg error: requiring pure function in solving differential equations

I'm trying to numerically solve 2 partial differential equations eq1 and eq2 given the boundary conditions in ...
0
votes
2answers
120 views

Poincaré Section

I have encountered somewhat the same problem as here. But with the equations, $x'(t) = p(t), p'(t) = - x(t) - y(t), y'(t) = q(t), q'(t) = - y(t) - x(t)$ My code is, ...
0
votes
1answer
183 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. ...
3
votes
1answer
145 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
1
vote
1answer
90 views

Need help solving a system of two 1st order nonlinear differential equations

The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = ...
3
votes
1answer
255 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
16
votes
4answers
740 views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
0
votes
0answers
39 views

DSolve solves PDE only without boundary condition, but fails otherwise

I'm trying to solve for Te[w, Pprobe, t] in a partial differential equation. What's surprising is that it manages to solve it when I don't put in any initial ...
0
votes
1answer
50 views

How to find the value of a solution of an ODE at a particular point [closed]

I'm trying to find the value of $z(y)$ at a particular time, say $y=0.5$. I've solved the differential equation. I tried using z3 = z[3] /. sol, but it's not ...
0
votes
1answer
144 views

Solving System of Nonlinear with Three Differential Equations

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
0
votes
1answer
144 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
47 views

EquationTrekker-like behavior for state space?

EquationTrekker is great for phase space plots, however I want to plot the results of $$\phi '(t)=-b \sin (\phi (t))+g \sin (\Phi (t)-\phi (t))+1\\\Phi '(t)=g y ...
3
votes
1answer
89 views

Already solved DE, now I need to rearrange and plot

I have solved for $z(w,x,y)$ in a differential equation: $$ 3\frac{\partial z}{\partial y} = 2(z-1) + (1-wy^2 )x $$ And I obtained the general solution: $z = f(w,x,y)$ Now putting in $x=0$, we have ...
0
votes
1answer
133 views

How do I subtract two contours?

Suppose I have this contour described by the equation the root $z$ of this equation $$ \frac{1}{x^2 + y^2} + \frac{1}{xz} = 2y $$ Now suppose the equation is tweaked slightly, with an addition of ...
1
vote
1answer
186 views

Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
35
votes
2answers
1k views

Numerically solving Helmholtz equation in 2D for arbitrary shapes

I would like to solve the Helmholtz equation with dirichlet boundary conditions in 2 dimensions for an arbitrary shape. (for a qualitative comparison of the eigenstates to periodic orbits in the ...
1
vote
1answer
45 views

Solved the differential equation, how to rearrange to find solution? [closed]

I have solved for values of $y(x)$ from $1 < x < 2$ and plotted them: ...
0
votes
2answers
66 views

Solve simple differential equation - Error?

I get the error "The function Te appears with no arguments." when running this code. I'm not sure why. Is it because of the $Abs[\Gamma]$ ? ...
2
votes
1answer
154 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 ...
0
votes
2answers
154 views

Plotting a solution of the Allee Effect

I am doing a project on the Allee Effect. I am able to successfully create a stability analysis. That is, I can find the relevant equilibrium points ($y_e = 0,\ y_e = \alpha$ and $y_e=k$) and draw ...
0
votes
1answer
100 views

DSolve problem with system of linear ODEs

I encounter a rather strange problem in Mathematica when trying to solve the following system of linear differential equations: ...
1
vote
0answers
142 views

Problem with NDSolve in Mathematica 9 / 10

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ...
3
votes
1answer
97 views

Is it possible to obtain explicit symbolic solutions to such linear ordinary differential equations?

The ordinary differential equations to solve have symbolic parameters $k_1,k_2,k_3,k_4,k_5,k_6 \in \mathbb{R}$. $$ \left\{ \begin{array}{l} {y_1}'(t)=-{k_1} {y_1}(t)-{k_2} {y_1}(t),\\ {y_2}'(t)={k_2} ...
9
votes
1answer
1k views

How to solve a system of partial differential equations?

Edit: since the upgrade to Mathematica 10, this problem seems solved I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} ...