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
240 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: ...
8
votes
2answers
416 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
550 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
175 views

WhenEvent “StopIntegration” problem

The first example on the WhenEvent help page is ...
0
votes
0answers
176 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
247 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
193 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
49 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 ...
51
votes
3answers
4k 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
40 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
247 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
274 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
847 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: ...
10
votes
1answer
314 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 ...
3
votes
1answer
177 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 ...
2
votes
0answers
247 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
4
votes
1answer
127 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] ...
3
votes
0answers
71 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 ...
1
vote
0answers
200 views

Solving PDEs with complicated boundary conditions

The system I'm trying to solve is $$\nabla^2 C_{(r,\theta)} =0$$ $$C_{(\infty,\theta)}=C_0$$ $$ [ \frac{\partial C_{(r,\theta)}}{\partial r} \cos(\theta)+\frac{1}{r}\frac{\partial ...
33
votes
3answers
2k 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 ...
5
votes
0answers
120 views

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

Bug introduced in 5.2 or earlier and persisting through 10.4.1. I encountered this when trying to solve this problem with DSolve: ...
1
vote
1answer
243 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 ...
10
votes
4answers
645 views

Should DSolve always return solution with constant of integration?

Bug introduced in 10.0.0 and 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
158 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
370 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, ...
2
votes
0answers
136 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; ...
3
votes
1answer
203 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
1answer
214 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
283 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
154 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 ...
2
votes
2answers
347 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 ...
2
votes
1answer
164 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
294 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 = ...
3
votes
0answers
262 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = ...
0
votes
2answers
287 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: ...
3
votes
3answers
1k 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
1answer
208 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
686 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
78 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 ...
1
vote
0answers
42 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 ...
1
vote
0answers
75 views

Coupled ODEs with boundary conditions - DSolve Error [closed]

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
222 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 ...
2
votes
2answers
583 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 ...
2
votes
1answer
479 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: ...
1
vote
0answers
309 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
59 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
100 views

Solving for variables that satisfy an equation

I have the following ...
2
votes
2answers
204 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
1answer
1k 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
1k 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 ...