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

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8
votes
1answer
128 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
17 views

Why MMA tell the arguments is not ordered consistently when I solve a simply linear PDE

I want to solve a simply linear PDE about p0 which is a function of Xi, Zeta and Tau. However, the boundary condition is defined at Zeta=h, which is a function of Xi and Tau. The other quantities are ...
0
votes
0answers
39 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
264 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
45 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
87 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
141 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
87 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
49 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
38 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
204 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
119 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
182 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
144 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
738 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
38 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
49 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
140 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
139 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
46 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
132 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
181 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
149 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
99 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
141 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
96 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} ...
1
vote
1answer
104 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: ...
1
vote
1answer
87 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
75 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, ...
2
votes
1answer
163 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 ...
4
votes
1answer
116 views

1/0 encountered when solving an ODE

What can cause this error to show up? Clear[lambda, a, b, x, y]; ode = lambda y[x] + a b y'[x] + a (-1 + b x) y''[x] + y''''[x] == 0; DSolve[ode, y[x], x] ...
25
votes
3answers
813 views

Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally ...
1
vote
1answer
542 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...