Tagged Questions

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

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5
votes
2answers
87 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
100 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
357 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
117 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: ...
2
votes
1answer
192 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
48 views

WhenEvent “StopIntegration” problem

The first example on the WhenEvent help page is ...
0
votes
0answers
53 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
0answers
111 views

Use Runga-Kutta method to solve a system of many ODEs [closed]

For my simulation purpose, I need to solve the following system of DEs using 4th-order Runga-Kutta (RK) method in Mathematica: $$ I_{k,0}'(t) = -\beta_1~I_{k,0}(t) + k~\lambda~ \Theta(t) + \gamma~ ...
1
vote
2answers
231 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 ...
2
votes
0answers
99 views

Edge finite elements in Mathematica [closed]

I am wondering if it's possible to extend the Finite Element capabilities of Mathematica so as to include other types of elements such as edge vector elements (Nedelec) which can be used in ...
1
vote
2answers
82 views
1
vote
0answers
34 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 ...
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 ...
0
votes
0answers
32 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
59 views

NDSolve solution methods issue

I´m modelling a biological reaction thorugh a set of differential equations. ...
4
votes
2answers
156 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: ...
5
votes
3answers
225 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: ...
7
votes
0answers
162 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
72 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
46 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
121 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
77 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
60 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
920 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
48 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
104 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
62 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
60 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 ...
8
votes
3answers
243 views

Should DSolve always return solution with constant of integration?

Version 10.0 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
88 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
109 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
127 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
57 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
86 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
145 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
132 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
81 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
64 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
165 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
61 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
126 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
134 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
49 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
77 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
275 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
42 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
147 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
305 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
68 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 ...