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

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0
votes
1answer
12 views

Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
1
vote
1answer
51 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in 10. Farad Micro Volt mean? ...
0
votes
0answers
30 views

Schrödinger equation for Hydrogen atom

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 ...
12
votes
1answer
343 views

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

The point is to solve the eigensystem of the given Hamiltonian. I tried ParametricNDSolve combined with FindRoot to search for ...
0
votes
1answer
53 views

How to solve the following GR PDE?

Someone could help me for solving the following GR PDE? (this code do not work yet) ...
0
votes
0answers
22 views

Boundary Conditions that depend on each other

I have to numerically solve some 4th order differential equations: B''''(r)=f(r,B,B',B'',B''',S,S'), S''(r)=g(r,B,B',S,S') I'm trying to use the shooting method ...
2
votes
1answer
168 views

Strange WhenEvent Behavior

Bug introduced in 10.3 or earlier and persisting through 10.3.1 or later Given: ...
2
votes
0answers
47 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 ...
1
vote
1answer
86 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: ...
2
votes
1answer
52 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. $$y_1''(x)=-\frac{1}{2} \left(x-y_1(x)\right)$$ $$y_2''(y)=-\frac{1}{4} \left(y-y_2(y)-5\right)$$ $$y_1(0)=y_2(1)$$ $$y_1(1)=y_2(0)$$ ...
3
votes
1answer
368 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
0
votes
0answers
50 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
393 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 ...
1
vote
1answer
70 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by ...
-2
votes
0answers
52 views

NDeigensystem returns complex non-hermitian error for the calculation of vibrations of a cantilever [duplicate]

We are trying to use NDEigensystem to solve for the vibration of a cantilever with a triangular cross-section. The relevant PDE is $\mu \nabla^2 \vec u + (\lambda + \mu) \nabla(\nabla \cdot \vec u) = ...
3
votes
0answers
49 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 ...
3
votes
0answers
33 views

WhenEvent and Resetting of Variable in PDE when operation succeeds

I have had success in using WhenEvent to reset or change a variable within NDSolve with ordinary differential equations. My ...
4
votes
1answer
84 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 ...
0
votes
0answers
51 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
1answer
110 views

solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...
1
vote
1answer
373 views

Numerical solutions of Gross-Pitaevskii equation [on hold]

I am trying to solve the Gross-Pitaevskii equation numerically and using NDSolve, but this seems to be a dead end. The problem is boundary and initial conditions ...
4
votes
0answers
48 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. ...
3
votes
1answer
68 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 ...
1
vote
1answer
30 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: ...
0
votes
0answers
55 views

Implicit differentiation dx/dt?

I am trying to find $\frac{\partial t}{ \partial y}$ as a function of $x$, $y$ and $\frac{\partial t}{\partial x}$ if both $x$ and $y$ depend on $t$ for the function ...
3
votes
1answer
61 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: ...
1
vote
1answer
92 views

Differential equation in two variables

I have a system of second order differential equations, with two independent variables, which represents a trajectory. I tried solving this system using NDSolve and ...
1
vote
1answer
55 views

Product derivative on derivative [on hold]

this is a silly question, probably. How to product derivative on derivative in Mathematica. I mean for example how to achieve this result: Just more explanation. I need this for solving task with ...
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] -> ...
3
votes
2answers
239 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
42
votes
2answers
1k views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
1
vote
1answer
97 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 ...
4
votes
1answer
1k 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
0answers
28 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 ...
0
votes
1answer
52 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 ...
0
votes
0answers
50 views

DSolve does not produce any answer [closed]

I want to solve the following differential equation, but Mathematica keeps Running without any result. DSolve[{Y'[t] == p - (a + bwt^(w - 1))*Y[t], Y[0] == 0}, Y[t], t] It is necessary to mention that ...
-1
votes
2answers
111 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. ...
10
votes
1answer
295 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 ...
0
votes
0answers
43 views

Diagnosing NDSolve misbehavior [closed]

I'm solving a simple first-order ODE depending on a parameter $\alpha$. I want to package the family of solutions $x(t)$ for each $\alpha$ into single function of two variables $x(t,\alpha)$, and to ...
3
votes
1answer
96 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 ...
7
votes
0answers
339 views

Problems when solving a nonlinear PDE system with NDSolve

The nonlinear PDE system is actually extracted from a research paper published in 2000 Here is the paper link The authors solved the system by using an ordinary differential equation integrator in ...
0
votes
1answer
48 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
106 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 ...
2
votes
1answer
72 views

NDSolve::depdole error

I'm trying to solve a pair of differential equations with NDSolve. They contain a discontinuous function bounce. I've trimmed ...
12
votes
1answer
189 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 ...
-2
votes
0answers
76 views

singularity or stiff system

I have tried to solve this rotating disk flow problem in Mathematica. However, I got errors. Why did Mathematica return this error, mind to explain and help me solving this kind of error? ...
1
vote
1answer
879 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? ...
1
vote
1answer
160 views

NDSolve There are fewer dependent variables, {V[S,t]}, than equation

I am trying to solve the BlackScholes PDE for Barrier option. It works fine for european barrier, but errors out on american boundary condition ...
0
votes
3answers
61 views

How to select coefficient of an exponential function

Suppose I have these set of equations: sol = DSolve[{ x'[t] == -RandomReal[]*x[t] + y[t], y'[t] == x[t] - *y[t] , x[0] == 1, y[0] == 0}, {x[t], y[t]}, t] The ...