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

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0
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0answers
24 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 ...
2
votes
1answer
32 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
33 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
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0answers
43 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 ...
1
vote
1answer
39 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
69 views

Define and refine mesh around a hole

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

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
2
votes
2answers
71 views
2
votes
1answer
86 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 ...
2
votes
0answers
27 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
71 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
88 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 ...
0
votes
0answers
34 views

Boundary Value Problem Errror [on hold]

I have a first order differential equation such as $\quad \quad d/dt (u[x,t]) = - u[x,t]\,u[x,t]$ with the boundary conditions $\quad \quad u[0, t] = 0,\ u[L, t] = 0$ where $x$ is between $0$ and ...
3
votes
2answers
59 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: ...
3
votes
2answers
130 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
64 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
2answers
90 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
49 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 ...
2
votes
0answers
57 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
142 views

Clicking phase plane with mouse

Here is what I have thus far: ...
3
votes
1answer
50 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
43 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
103 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
76 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
46 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
58 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
123 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
68 views
1
vote
1answer
36 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
71 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 ...
1
vote
0answers
39 views

Disease Network Model Using NDSolve

I have a basic disease model using NDSolve: ...
1
vote
1answer
59 views
0
votes
0answers
41 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
44 views

Phase Portraits

If possible I want to create several phase portraits like this: ...
0
votes
1answer
37 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
77 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 ...
7
votes
3answers
277 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 ($y\neq0$) ...
-1
votes
0answers
55 views

How can I solve my differential equation?

I am using Dsolve to solve this PDE, but it does not work. Can anybody help me? My equation: $y'(x)^{1/N} + x\ \frac{d}{dx} (y'(x)^{1/N}) - (y/x)^{1/N} = - A P/(2 ...
1
vote
2answers
48 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: ...
7
votes
2answers
276 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
0
votes
3answers
88 views

Delay difference equation

How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations? For example if I want to "see" the values ...
0
votes
2answers
55 views

Using parts of piecewise function

I define: f[x_] := Piecewise[{{5, 0 <= x < 10}, {g[x], 10 <= x < 15}, {h[x], x > 15}}] Then I try to solve ODE: ...
3
votes
1answer
127 views

How to solve Laplace equation in 3D?

Basically I want to solve Laplace equation for truncated octahedron in a cube matrix. The boundary condition is Concentration u=200 at surface of truncated octahedron and u=15 at boundary of cube. I ...
5
votes
0answers
69 views

DSolve giving strange error messages solving a PDE

Consider this set of PDE $$\left( x^{2}+y^{2}\right) \dfrac {\partial u}{\partial x}+n x y\dfrac{\partial u}{\partial y}=0$$ have general solution $$u\left( x,y\right) =f\left( \dfrac {1}{n-1}\dfrac ...
0
votes
1answer
99 views

Implicit differentiation and the Folium of Descartes [duplicate]

Given the function (Folium of Descartes) $x^3 + y^3 = 3xy$, how would I find the equations for tangent and normal lines at the point $\left( \frac{3}{2},\frac{3}{2} \right)$? I know that I must use ...
0
votes
1answer
70 views

Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any ...
-2
votes
0answers
39 views

How can I use the Euler's method to approximate $xy′ + y = e^2,\, y(1) = 2$? [duplicate]

I've been using the while syntax but it doesn't work.