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

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8
votes
2answers
731 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
427 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
189 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
198 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
372 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
94 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 ...
4
votes
1answer
301 views

Fitting numerical model to experimental data

I have diffusion equation with the initial/boundary conditions: ...
13
votes
2answers
1k 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
169 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
103 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
144 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
51 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
162 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
79 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
votes
0answers
107 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
130 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
131 views

NDSolve solution violates initial conditions

I have the following code: ...
2
votes
0answers
137 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 ...
5
votes
4answers
740 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
349 views

How can I apply calculus to functions obtained from NDSolve?

Originally, I asked the question below, but the real underlying issue is as follows: When we solve an ODE numerically, I get the answer like this: ...
2
votes
1answer
96 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
5
votes
2answers
148 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 ...
1
vote
1answer
134 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) = ...
0
votes
0answers
78 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 ...
2
votes
0answers
65 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
237 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 ...
3
votes
1answer
106 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 ...
5
votes
1answer
512 views

How to solve fluid flow problem based on Navier-Stokes equations?

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
0
votes
2answers
79 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 $Abs[\Gamma]$ ? ...
6
votes
2answers
2k 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
412 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
149 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
223 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: ...
1
vote
1answer
228 views

Using spherical derivatives with NDSolve

I am trying to plot the path of an object around a centre of mass. Obviously this needs spherical coordinates. The problem I encounter is with the derivatives. The Derivatives in spherical coordinates ...
5
votes
2answers
115 views

Automatically detect largest interval over which NDSolve can find a solution

Question: Consider the following numerical resolution: NDSolve[eqn, {x1[t], x2[t], y[t]}, {t, tmin, tmax} where eqn, ...
3
votes
1answer
124 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} ...
1
vote
1answer
920 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: ...
1
vote
1answer
161 views

When plotting vector fields what is the difference between the following?

I am a new Mathematica user, and I have run into a question. What is the difference between the output of the commands: ...
6
votes
2answers
291 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
2
votes
1answer
314 views

Solve ODE $d^2u/dx^2 + u/A = 0$

How can I solve following ODE with Mathematical: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ with the conditions: $$ \left.\frac{d^2u}{dx^2}\right|_{x=0} = 0, $$ $$u(x=0) = B$$ and ...
1
vote
1answer
100 views

WhenEvent “StopIntegration” problem

The first example on the WhenEvent help page is ...
0
votes
0answers
110 views

NDSolve with Table and Boundary Conditions

I am trying to implement a 1D model of coupled field equations where I split up space into pieces to get a system of coupled ODEs which I call Eeqns and Ieqns. The problem I can't figure out is how to ...
1
vote
2answers
242 views

How do I plot the differential of this function?

Suppose I have this function: $$z(x,y) = \left| \frac{ \frac{1}{3x +iy} -2x}{iy + \frac{1}{x}} \right| $$ I want the contour plot of $\frac{\partial z}{\partial x}$ with axes $(x,y)$. Tried this ...
1
vote
2answers
120 views

How do get an output table or a plot of individual variables from NDSolve output

I have the following equations and settings: ...
1
vote
0answers
48 views

How to fit data with numerical solution of system of parametric ODE? [duplicate]

I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function ...
47
votes
2answers
3k 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 ...
0
votes
0answers
35 views

How can Mathematica solve 7 equations and want to find 7 variables [duplicate]

I have 7 equations as below * e1 := (1 - a) p Subscript[A, 0] Subscript[s, K ] ! *SubsuperscriptBox[(s), (L), (-a)] = (1 - b) Subscript[B, 0] (1 - Subscript[s, K]) (1 - Subscript[s, ...
-1
votes
1answer
140 views

How to get solution from DSolve

How to get the solution from DSolve in such way that there is no need to copy the result. When for example solving: ...
4
votes
2answers
224 views

NDSolve fails to solve vector-valued function x'[t] == a . x[t] + u . b

I get no solution when I run the following command: ...
6
votes
3answers
569 views

Can NDSolve handle discountinuos data?

It is possible to numerically solve a differential equation if not-smooth data are involved? For example the following instruction return the error NDSolve::bvdisc: ...