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

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7
votes
0answers
169 views

Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
2
votes
1answer
78 views

NDSolve: EventAction list specification using Table fails

I have an NDSolve problem that needs a list of a large number of events that are generated programmatically. Here is a simple example that demonstrates the problem on Mathematica 7 and 8 (the versions ...
0
votes
0answers
48 views

Complex infinities in an Euler-Lagrange equation

I now wish to solve for $L(t)$ and $H(t)$ some ugly Lagrangian (in the code below) in configuration space, respectively the length and the height of a system. I tried running the code below, with the ...
4
votes
1answer
122 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] ...
0
votes
0answers
92 views

Plotting Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near a rotating black hole (given by the Kerr solution) which involves a system of first order differential equations. Some Context (not ...
3
votes
0answers
63 views

Error solving third order ODE in version 10. No error in V9. DSolve`DSolveKovacicDump`

This is an ode which is solved with no error in V9, but gives a very strange error in V10. Is this a regression bug? On version 9, the ode is solved with no error ...
25
votes
3answers
955 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 ...
2
votes
0answers
51 views

DSolve breaks when the ordering of independent variables aren't proper?

I encountered this when trying to solve this problem with DSolve: ...
1
vote
1answer
112 views

Use NDSolve to solve a PDE

I have the following PDE (a master equation, and $P$ is probability density, $0\le x\le1$ and $0\le y\le1$): $$ \partial_t P(x,y,t)=x\partial_xP(x,y,t)+(1-y)\partial_yP(x,y,t)+2P(x,y,t) $$ The ...
0
votes
0answers
63 views

Trouble outputting Plot

I am trying to solve a system of ODEs and plot them with Manipulate but I keep getting blank outputs. Below is my code: ...
1
vote
0answers
76 views

solution of differential equation with complex roots [closed]

How to find the solution of differential equation with complex roots For example of [{y^2 n[t]+ 2 k y n'[t] + n''[t]= M p sin(o t), n[0]==0, n'[0]==0}, n,t] given k lies between 0 to 1 which makes the ...
9
votes
4answers
272 views

Should DSolve always return solution with constant of integration?

introduced in Version 10.0, fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
4
votes
1answer
101 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} ...
1
vote
0answers
124 views

Speeding up NDSolve for system of differential equations

I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ...
1
vote
1answer
178 views

Numerical solution NDSolve for SIR model [closed]

I'm trying to numerically solve the SIR model. This should be simple but I'm can't understand why this is not working: ...
2
votes
0answers
66 views

Apply IC and BCs on Second - Order Linear PDE

I am now trying to solve second - order linear partial differential equation in that interested eq. has been separated into variables to simplify the procedure for Mathematica. Here is my equation; ...
2
votes
1answer
91 views

Why DSolve giving Inconsistent or redundant transcendental equation on this problem

Kamke's differential equation #574 has a solution, but Mathematica generates an error message as it tries to solve it. It still gives the solution. My question is: What could have caused Mathematica ...
0
votes
0answers
28 views

How DSolve with a multisymbol function argument

I used DSolve on a differential equation e got the following result: You may notice that C[ 1 ] is a function of the variables r and z in a defined form. If I substitute this result in my ...
0
votes
1answer
147 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 ...
0
votes
2answers
138 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
0answers
90 views

Optimizing a functional using variational calculus

Here I am, trying to get the trajectory $(x(t),y(t))$ that will minimize the following Lagrangian (i.e. the integrand of the functional) between $(-1,-1)$ and $(-1,y_{eff})$ where $x_{eff}$ is defined ...
0
votes
0answers
67 views

Help to plot Poincare section for a system of delay differential equations

I'am trying to plot Poincare section for a 4-dimentional system of Delay differential equations. I don't know how to specify initial conditions. Can I use each of the code in the following ? Also how ...
3
votes
2answers
172 views

Problem with Poincare section

these are equations for some double oscillators: $x'(t)=p, p'(t)=-x-3y, y'(t)=q, q'(t)=-y-3x$ I would like to plot the Poincare section for collection of $(y,q)$ when $x=0$ and $x'(t)>0$ (or for ...
0
votes
0answers
68 views

Energy Equation: Boundary and initial condition

I'm trying to solve the energy equation and NDSolve is able to solve the problem. Even though the result is acceptable, I have always the warning "boundary and initial conditions are inconsistent". ...
2
votes
1answer
133 views

Simple differential equation to solve

Suppose we have this differential equation: $$ x^2 + y^2 + z^2 = \frac{\frac{\partial y}{\partial x}}{x+y+z}$$ I want to find $\frac{\partial y}{\partial x}$ at x=1,y=1,z=1. I tried this code but ...
0
votes
2answers
142 views

Solve differential equation with 3 variables and plotting contour

Suppose we have this equation: $$ 2 - x g(z) f \left(x, \frac{\partial y}{\partial x}\right) = 3y $$ using initial condition $y = 2$ where $g = \left| \frac{3}{2-iz} \right|$ and $f = ...
0
votes
0answers
55 views

Ndsolve, transmission line transients

I am trying to use NDSolve to analyze transients in transmission lines. I started with this simple one: ...
0
votes
2answers
82 views

Plot integration curve of a system of ODEs

I'm really n00b in Mathematica, so please bear with me, as this seems to be my only option to learn how to do what I wany to do. I have a system of two differential equations: ...
2
votes
3answers
300 views

Implicitly differentiate an equation, then solve the resulting equation

Suppose I have an extremely tedious equation to differentiate and want mathematica to help do the differentiation and solve. Consider a less tedious equation: $$y (x,z) = sin \left(\frac{1}{x} ...
0
votes
0answers
46 views

Pass model parameters to NDSolve'Reinitialize

I am wondering if there is a way to pass parameter values during the NDSolve'Reinitialize step of the NDSolve process? I've read that one way to possibly speed up repeated calls to NDSolve is to ...
0
votes
1answer
156 views

Numerical solution of the hyperbolic equation

I am trying to solve the following hyperbolic equation with given boundary conditions: I choose as initial condition $u=1$, and evolve the above hyperbolic equation until reaching a stationary ...
4
votes
1answer
328 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + ...
0
votes
1answer
70 views

Unexpected behaviour plotting a PDE solution

I'm solving some coupled PDEs (Eb1 and Ef1) and what I plot for Eb1 appears to be correct. However, for some reason, when I go to plot Ef1, I get nothing. MWE is below (beginning is constants and ...
0
votes
0answers
108 views

Im trying to model balls in a box with NDsolve, but the balls keep escaping the box

This Code produces a box filled with balls at different positions with random charges on them and then calculates their motion according to Coulombs law. rendering the electric field as well as the ...
1
vote
0answers
33 views

Compiled NormFunction

I would like to use a user-defined NormFunction with NDSolve, e.g., NormFunction -> (Norm[Take[#, 2], \[Infinity]] &) which says that the infinity norm ...
0
votes
0answers
50 views

Coupled ODEs with boundary conditions - DSolve Error

I'm relatively new to mathematica and I can't find the error here. I suspect it has something to do with the fact that vx, vy, vz aren't blue on my mathematica - as in, they already have some assigned ...
1
vote
1answer
122 views

Liouville theorem demonstration

My goal is to create a demonstration of the Liouville theorem in 2D phase space. I made up an interesting potential energy function $U(x) = (x-4)x^3 + 27$, so that the minimal energy of system is ...
1
vote
2answers
162 views

Trying to model Heat flow trough different materials with NDsolve

What I'm trying to achieve is model of the heat flow, in this case for the simplest 1D case,its relatively easy to do for the steady state case, but when I try to do it with NDsolve so I get the ...
1
vote
1answer
174 views

Finding the eigenfunctions of one and two dimensional Harmonic Oscillator

(Edited) For finding the ground state wave function of: $ H\psi(x) = (-1/2)d^2\psi(x)/dx^2 + (1/2)x^2\psi(x) = E \psi(x)$ I have written: ...
0
votes
0answers
120 views

Problem With NDsolve trying to simulate n-body-gravity problem

Im Trying to model a cloud of point masses that act according to gravity, what im strugeling with is the exclusion of cases where euclidian distance = 0, If I try to do it with an If statement in my ...
1
vote
0answers
144 views

How to find a particular solution using NDSolve

I'm looking for a way to find a specific solution to a differential equation. As a simplified version of my problem, here's a similar setup for a simple harmonic oscillator problem. ...
0
votes
0answers
57 views

Showing Steps of Calculations [duplicate]

I'm solving a a differential equation in Mathematica and was wondering how to show the steps, like how Wolfram|Alpha does it, in the program. Any ideas?
0
votes
0answers
85 views
2
votes
2answers
123 views

Looking for an elegant way to solve a (system of) ODEs/functional equations with undetermined coefficients

I want to solve an ODE using undetermined coefficients/guess-and-verify and am looking for an elegant way to use this technique. I am running into a few ugly warts. Here is a basic implementation for ...
0
votes
0answers
68 views

Solving a Partial Differential Equation

I am trying to solve the following PDE: ...
0
votes
0answers
83 views

NDSolve :: ndode error while solving an coupled ODEs

I have a scenario where in trying to solve for the ground-state of a Hamiltonian, I require to be able to solve some coupled differential equations. Prior to this I have already set k=1 and Δ=5 $$ ...
0
votes
1answer
636 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 ...
1
vote
2answers
317 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
6
votes
3answers
388 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
2
votes
1answer
214 views

Euler's method for a 2nd order ODE

This is my first post on this site. Also, I'm new to Mathematica. I'm trying to solve my first problem with Mathematica. It's about solving a 2nd order differential equation. I dont have the explicit ...