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

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7
votes
2answers
330 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
0
votes
0answers
62 views

Kovacic's algorithm

Kovacic’s algorithm is used to find out whether or not an ODE has a Liouvillian solution, and if it has, then what that solution is. My question is: Is there any code written in Mathematica for ...
0
votes
1answer
41 views

Getting error when trying to solve two coupled differential equations with NDSolve

Mathematica newbie here. I have been trying to use NDSolve to solve two coupled differential equations. Each equation on its own (minus the coupling terms) solves ...
0
votes
0answers
75 views

Coupled PDEs with discontinuous boundary conditions?

So I have a system of coupled PDEs that represent the movement of an interface of fluid. The interfaces are functions of time and space, ie. $h_1(x,t)$, $h_2(x,t)$, $h_3(x,t)$. The PDEs are horrendous ...
4
votes
1answer
77 views

Solving PDE involving Hilbert transform numerically

I'm trying to solve the following equation numerically: $$u_{tt}-\mathcal{H}(u_x)=A^2_{xx},$$ where $\mathcal{H}$ is the Hilbert transform and $A$ is a prescribed forcing function which we assume ...
1
vote
1answer
208 views

Using the Levenberg - Marquardt algorithm to minimize a user-defined function

I wrote a function in Matlab that optimizes another user defined function using lsqnonlin with 'levenberg-marquardt' option. Now, I'd like to use the first to ...
3
votes
1answer
86 views

Cylindrical GL Equations

I am trying to solve numerically the GL equations in cylindrical coordinates. I already know what the shape of the solutions to these equations should look like, but I am not able to get the correct ...
0
votes
0answers
58 views

Weird error message when using differential-algebraic solver in NDSolve

Since the most recent version NDSolve's built-in methods so far do not work properly, in order to solve the nonlinear partial differential equations here, an ...
3
votes
0answers
80 views

Measuring Temp on a cubical using heat equation with Neumann and Dirichlet boundary conditions

I'm trying to solve 3D heat equation to understand how the temperature varies with time on cubical. i have mixed boundary conditions: Dirichlet on the bottom surface (constant Temp) Neumann on all the ...
4
votes
2answers
101 views

Why is NDSolve's StartingStepSize with ExplicitEuler not working? How do I set the step size?

Why do I get a smooth curve (that is obviously wrong) when I run this? ...
3
votes
1answer
51 views

How can I manage discrete variables that oscillate when using NDSolve?

I have a system of differential equations with two discrete variables (var1 and var2) that can be either 0 or 1. I'm trying to ...
0
votes
1answer
92 views

Problem with solving an optimal control system with Shooting Method

I try to solve a system of differential equation by shooting method. I looked at questions asked on the site but I could not find that could help me. My functions are ; ...
4
votes
1answer
270 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
3
votes
1answer
125 views

NDSolve for optimal control theory

For an optimal control problem, I need to solve a differential equation in which (a) the system is formulated according to a function and (b) initial/terminal conditions are discontinuous. Here is an ...
1
vote
1answer
130 views

NDSolve: Indeterminate expression 0. ComplexInfinity encountered? [closed]

The following code give errors that I don't understand. Could you please suggest a method to solve these differential equations? ...
0
votes
0answers
60 views

NDSolve: problem due to boundary conditions

I am trying to solve a 2nd order ordinary linear differential equation (DE==0). Here is the code: ...
10
votes
0answers
109 views

Differential equations with rational functions as solution

I have some families of nonlinear, first order differential equations. When I try to use DSolve, I usually get a mess (if anything at all) in terms of ...
1
vote
1answer
69 views

Partial differential equation with infinity limit

How do I get Mathematica to solve the following partial differential equation $$ \frac{\partial u(y,t)}{\partial t} = \nu \frac{\partial^2 u(y,t)}{\partial y^2}+\frac{\partial U_0(t)}{\partial t}$$ ...
3
votes
2answers
107 views

Reaction-diffusion PDE with NDSolve: either very slow or very inaccurate

I am struggling to have Mathematica 10.3 solve a system of PDE's (with periodic boundary conditions and random initial conditions), but either it produces a set of very noisy InterpolatingFunction ...
2
votes
1answer
99 views

Solve and plot differential equation

I want to solve this differential equation $\qquad y'(x)=\frac{x-y(x)}{1-y(x)-x}$ and plot it's solution. But DSolve doesn's work. ...
2
votes
1answer
120 views

How to handle a special Neumann-like boundary condition in NDSolve?

How to solve the following nonlinear ODE with two algebraic equations and one boundary condition? ...
1
vote
1answer
65 views

To find a limit cycle with period 1 in NDSolve

I am trying to find a limit cycle with period 1 of an ode system. The idea is to compare the values of the system during two periods, for example, ...
0
votes
1answer
52 views

Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
2
votes
0answers
139 views

Schrödinger equation for Hydrogen atom [closed]

I'm trying to solve Schrödinger 1D equation for hydrogen atom but I found several difficulties. To get in context I want to solve this equation For Z and l real and arbitraries. To start with I ...
0
votes
1answer
88 views

How to solve the following GR PDE?

Someone could help me for solving the following GR PDE? (this code do not work yet) ...
2
votes
1answer
75 views

How to solve two ODE differential equations, numerically, with four dependent boundary condition

I have two ODE differential equations(DE) and four dependent B.C. $$y_1''(x)=-\frac{1}{2} \left(x-y_1(x)\right)$$ $$y_2''(y)=-\frac{1}{4} \left(y-y_2(y)-5\right)$$ $$y_1(0)=y_2(1)$$ $$y_1(1)=y_2(0)$$ ...
0
votes
0answers
63 views

How to define an exclusion zone for NDSolve

I need to numerically integrate a differential equation and define two exclusion zones to stop the integration. The Mathematica code looks like this : ...
11
votes
3answers
506 views

Using NDSolve to find particle trajectory

I'm trying to simulate a particle in an electric and magnetic fields, but numerically instead of analytically. This is basically solving the equation $$q \cdot \left(p'\times B\right) + q\cdot E = m ...
2
votes
0answers
71 views

NDeigensystem returns error due to mesh discretization when calculating vibrations of a cantilever

There was an transcription error in the code I provided in a previous post: NDeigensystem returns complex non-hermitian error for the calculation of vibrations of a cantilever This resulted in it ...
4
votes
0answers
65 views

WhenEvent and Resetting of Variable in PDE when operation succeeds [closed]

I have had success in using WhenEvent to reset or change a variable within NDSolve with ordinary differential equations. My ...
0
votes
0answers
60 views

Fourier-style solutions to differential equations, not piecewise polynomials

NDSolve returns piecewise polynomials. Is there any way I can get a single (non piecewise) function consisting of sines and cosines instead? Sort of a "Fourier approximation" to the solution of my ...
2
votes
0answers
41 views

Changing from Cartesian to polar coordinates in partial differential equation [duplicate]

I have a partial differential equation: $$\left(x^2+y^2\right)\frac{{{\partial ^2}u(x,y)}}{{\partial {x^2}}} + x^2\frac{{{\partial ^2}u(x,y)}}{{\partial {y^2}}}=0$$ How to change from Cartesian to ...
4
votes
1answer
90 views

System of equations is solved by NDSolve over just a tiny domain

I'm solving numerically a system of differential equations with the use of NDSolve. The numerical integration works only a very small interval of the argument. I'm ...
1
vote
1answer
43 views

Issue plotting PDE solution with manipulate

I am trying to plot the solution to the following PDE with the help of mathematica, however, when trying to employ manipulate to animate the behavior, I find that if I try this: ...
4
votes
0answers
58 views

Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain

I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ...
4
votes
1answer
77 views

How can I numerically pre-compute an indefinite integral with a parameter?

Suppose I have a function $f(t)$, and I want to compute its indefinite integral $$F(t)=\int_0^tf(\tau)\mathrm d\tau.$$ Moreover, suppose that, for any of a number of reasons, I require this integral ...
3
votes
1answer
68 views

Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
0
votes
0answers
19 views

Solving a simple ODE [duplicate]

I am trying to solve $y(x)' = \sqrt{y(x)}$ with initial condition $y(0)=0$ for $x\in \mathbb{R}$. I have tried this: DSolve[{y'[x] == Sqrt[y[x]], y[0] == 0}, y[x], x] but this gives {{y[x] -> ...
4
votes
2answers
253 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
3
votes
0answers
56 views

Weird behaviour for a vector InterpolatingFunction inside an NDSolve

I have run into some weird behaviour on the part of NDSolve which I find pretty bizarre and which I would like to understand better. Suppose, for the sake of ...
1
vote
1answer
138 views

NDSolve memory usage

I am trying to solve numerically a system of linear ODEs with some quickly varying driving functions. The basic command is: ...
1
vote
0answers
29 views

Nonlinear coefficients are not supported in this version of NDSolve [duplicate]

Thanks to the answers in other questions, I am aware of the fact that NDSolve produces Nonlinear coefficients are not supported in this version of NDSolve when some boundary conditions are ...
1
vote
1answer
119 views

Phase Portrait to Differential Equation [closed]

I posted this question on Math.SE and have received a satisfactory answer in the context of that website. I am re-posting it here to get input from Mathematica users. Why would I receive a different ...
0
votes
1answer
55 views

$4$-d system of second order PDEs

I have a $4$-dimensional nonlinear system of second order PDEs with periodic boundary conditions. Let $y(t,x)=(y_1(t,x),...,y_4(t,x))$ with $t \in \mathbb{R}$ and $x \in [0,1]$ then the system is ...
3
votes
1answer
174 views

Solve a nonlinear PDE equation with a Neumann boundary condition

I am trying to use Mathematica 10 to solve a PDE $$u_t=u_{xx}+u_{yy}+u(1-u),$$ in the unit disk $(x,y) \in D=\{(x,y):x^2+y^2<1\}$, with the Neumann boundary condtion $$\frac{\partial u}{\partial ...
0
votes
1answer
94 views

Trouble solving a system of 2 ODE's with NDSolve

I'm trying to solve a system of two coupled second-order ordinary differential equations using Mathematica's NDSolve. The functions of r that appear in the equations are ...
1
vote
3answers
121 views

Plot multiple functions with different but overlapping intervals

Suppose I numerically solve a differential equation by using sol = ParametricNDSolve[{y'[x] == b y[x], y[0] == 1}, y, {x, 0, 0.3}, {b}] And then I want to plot ...
-1
votes
2answers
122 views

Solving a quasi- or nonlinear PDE

Is the following PDE solvable in mathematica 9? When i solve it, the DSolve command does not do anything. ...
16
votes
1answer
494 views

How to numerically solve a 1-d time-independent Schrödinger equation?

The point is to solve the eigensystem of the given Hamiltonian. I tried ParametricNDSolve combined with FindRoot to search for ...
14
votes
1answer
278 views

Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square

I have recently been plotting eigenfunctions of the laplacian over the unit square using the NDEigensystem command. However, I have noticed something in the plots ...