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

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5
votes
1answer
141 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
0
votes
0answers
68 views

find initial condition for NDSolve

I have a complicate second order differential equation to solve numerically (too complicate to be posted). Unfortunately I do not know the behavior of the solution $\theta(r)$ near $r=0$ and I am not ...
1
vote
1answer
124 views

Poisson PDE in a rectangular domain

I found a solution for this problem, but this is in Scilab and I never use Scilab. Can anyone can help me to translate it in Mathematica? Here is the Link:http://imechanica.org/files/TorqueR.pdf I ...
0
votes
0answers
44 views

Trying to plot solution curves on top of a direction field

I'm trying to do some diff. eq. homework that requires taking a general solution to a differential equation and graphing a series of possible solution curves over a direction field of the general ...
4
votes
2answers
125 views

Vector form using NDSolve

Michael E2 wrote a wonderful solution for my question. Now I am considering the system: $$ \begin{align*} x'&=x^2 y,\ x(0)=1\\ y'&=-x y^2,\ y(0)=1 \end{align*} $$ I am wondering how I can ...
1
vote
0answers
68 views

NDSolve Poisson PDE for rectangle with hole

When I solved the Poisson PDE with function NDSolve in a rectangular domain with hole in the center, and search the first derivative with x and y why appear these protrusions on the diagram around the ...
0
votes
0answers
138 views

Laplace PDE in a polar coordinate system

I want to solve a Laplace PDE in a polar coordinate system with finite difference method, but I have a problem with boundary conditions at r = 0. Here is what I ...
0
votes
0answers
65 views

Stress calculation for stokes equation in 2D

I am solving the Stokes equation for the creeping flow, in a particular geometry, using the stream function formulation. This is my domain: ...
2
votes
1answer
122 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
3
votes
1answer
111 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
1
vote
0answers
51 views

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
2
votes
2answers
110 views
2
votes
2answers
134 views

Fighting the Current

I am working a problem I am working on. A boat start across a river at the point (c,0) and points its bow directly across the river to the point (0,0). The parameter a is the river current velocity, b ...
0
votes
1answer
88 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
2
votes
0answers
64 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
1
vote
1answer
92 views

DSolve for a huge linear inhomogeneous ODE in parallel

I have a linear inhomogeneous ODE with constant coefficients, which I need to solve symbolically. The problem is that the inhomogeneity is sum of more than 100 terms (however, each term itself is ...
1
vote
1answer
265 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
6
votes
1answer
97 views

Solving a PDE with a spatially piecewise-constant material parameter

I would like to solve equation for the 2D distribution of an electrical potential in the conductive medium: $$\nabla\cdot(\sigma\nabla f) = 0$$ where $f=f(x,y)$ is the electric potential (in 2D) and ...
3
votes
2answers
99 views

Memory Problem with Modules and NDSolve

I'm using NDSolve inside a module, and I appear to have a memory leak. The relevant code is: ...
4
votes
2answers
190 views

NDSolve in Mathematica won't use all the cores avaiable

When I solve a system of differential equations in Matlab, the task manager shows that all the CPU cores are in use. This is not true when I solve the same system in Mathematica. I have six cores. ...
1
vote
1answer
126 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
0
votes
1answer
132 views
0
votes
2answers
125 views

Solving differential equations with Wolfram Mathematica

So i saw this differential equations in my textbook $\frac{{{d^4}\omega }}{{d{x^4}}} + 4{\lambda ^4}\omega = 0$ and i figured why not solve it with majestic Wolfram Mathematica, so i write this ...
1
vote
1answer
67 views

Entering an differential equation in a Manipulate box

Does anyone have an example of a Manipulate demonstration where the user can type into a box the differential equation, time interval, initial condition, and the result is plotted? This possible in ...
3
votes
0answers
87 views

Differential Geometry on a MeshRegion

For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke there somewhere) use it to calculate coordinate ...
7
votes
2answers
160 views

Clicking phase plane with mouse

Here is what I have thus far: ...
3
votes
1answer
62 views

NDSolve with known tolerance function

I would like to solve the differential equation: y'[x]=F[y[x],x] with y[0.5]=y0 and x ...
0
votes
1answer
126 views

NdSolve problem :NDSolve::ndode: Input is not an ordinary differential equation

I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below. Not so sure about the boundary values that depends on R (M(0)=0, n(1)=0) ...
2
votes
1answer
231 views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda ...
2
votes
1answer
167 views

Nullclines and equilibrium point labels

I am trying to draw the vector field, nullclines, and equilibrium points for the system $$ \begin{align*} x'&=2x-y+3(x^2-y^2)+2xy\\ y'&=x-3y-3(x^2-y^2)+3xy \end{align*} $$ I have completed ...
0
votes
0answers
47 views

Having trouble reading this output (pure functions) [duplicate]

I'm after decoupling some odes and trying to solve them using mathematica but my output is in terms of Functions and InverseFuntions and I'm afraid I have no idea how to translate the output into ...
4
votes
1answer
88 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
2
votes
1answer
192 views

Coupled non-linear differential equations

I have a system of coupled nonlinear differential equations to solve: $$ \frac{\partial m(x,t)}{\partial t}+v(x,t)\frac{\partial m(x,t)}{\partial x}=-\gamma \frac{\partial^2 v(x,t)}{\partial x^2}, \\ ...
0
votes
1answer
82 views
1
vote
1answer
46 views

Value of event function not a real number

I am having some problems with handling an event during NDSolve. The event itself is simple, I am looking for when one of my coordinates, defined in ...
1
vote
0answers
88 views

Linear System with Complex Eigenvalues

My students will need to do the following work by hand. \begin{align*} x_1'&=-\frac14x_1+2x_2,\quad x_1(0)=1\\ x_2'&=-8x_1-\frac14x_2,\quad x_2(0)=1 \end{align*} They set it up in matrix ...
4
votes
1answer
205 views

Very slow mathematica finite differences

I have a simple code which solves an equation by an explicit method (FTCS). It takes mathematica several minutes (mathematica 10.0.2) to finish the calculation while the same code in Fortran runs less ...
1
vote
0answers
91 views

Disease Network Model Using NDSolve

I have a basic disease model using NDSolve: ...
1
vote
1answer
91 views
0
votes
0answers
44 views

Two identical expressions for ODE, two distinct result

I have a problem in solving ODEs: two identical expression provides me different answers! I have no idea what's going on, can any one give me some reason why the following two expressions are ...
0
votes
0answers
55 views

Phase Portraits

If possible I want to create several phase portraits like this: ...
0
votes
1answer
48 views

Simplify huge output or using the output without showing it in full [closed]

I'm trying to solve a system of differential equations. It works fine but Mathematica creates a huge output, which, when shown in full, results in a file size about 100 mb. Using Simplify doesn't work ...
0
votes
0answers
27 views

Substitution employed to DSolve [duplicate]

How do we get Mathematica to express generally what substitution has been employed in obtaining DSolve outputs? e.g.for solving particular: $ \int \sqrt {\sin^{-1} {\sqrt x }}dx $ EDIT1: ...
0
votes
0answers
83 views

Finding roots by solving its ODEs [duplicate]

Roots of fluctuating function (p,q real) needed to evaluate eigenvalues of $$ y(x) = \dfrac{\sin px }{p} + \dfrac {\sin q x }{q} =0 ...(1*) $$ form a real and complex infinite set. The way to ...
0
votes
1answer
32 views

Defining a function then using it in DSolve

Probably a pretty simple question but I've been stumped for awhile looking around. I'm trying to solve four diff. eq.'s using DSolve and some of these equations depend on a function B[t] which I try ...
7
votes
3answers
291 views

Find the eigenvalues for an ODE

For example, say I have $y'' + \lambda y = 0$ and the endpoint conditions are $y'(0) = 0$ and $y'(\pi) = 0$. How can I find the values for $\lambda$ that for which there is a non-trivial ($y\neq0$) ...
0
votes
0answers
53 views

NDSolve: basic settings for PDEs

I am trying to learn how to solve PDEs in Mathematica in order to deal with relatively simple problems without needing to formulate weak formulations in FreeFem++, which is rather time consuming for ...
1
vote
2answers
61 views

Using manipulate with a defined funtion to solve a ODE

As many in this community I'm new in Mathematica and while exploring the numerical solver for differential equations, I tried: ...