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

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-1
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0answers
45 views

Limitation of MMA in solving complicated functions?

I try to solve nonlinear PDE functions with NDsolve and NDIntegrate in MMA. And it seems that MMA will not work if the functions become too complicated. I do not know why. Below are my codes which ...
1
vote
1answer
155 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 ...
4
votes
0answers
66 views

Dealing with a nonlinear PDE using FEM

As far as I can see in the Mathematica documentation center, there are no built-in ways for solving nonlinear PDEs using Finite Element Method (FEM). I am dealing with a simple nonlinear ...
1
vote
1answer
39 views

Asymptotic Radial Wave Equation

I'm trying to reproduce the following solution to the ODE, $$\frac{d^{2}u}{d\rho^{2}} = \frac{l*(l+1)}{\rho^{2}}u$$ Solution: $$u\left(\rho\right) = C\rho^{l+1}+D\rho^{-l}$$ What I've tried in ...
0
votes
2answers
54 views

Using an interpolating solution of NDSolve into an algebraic expression

I would like to use the interpolating solution of NDSolve into an algebraic expression without creating a system of a differential equation and algebraic equation. The example is the following, the ...
0
votes
0answers
23 views

How to embed NIntegrate inside NDSolve to solve complex functions? [on hold]

I try to solve complex nonlinear PDE functions with intergrations using NDSolve in Mathematica, but failed. To simplify my problems, I wrote the following codes, but it does not work. ...
0
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0answers
33 views

How to use NDSolve for mixed types of several equations?

I have three equations, one is partial differential equation and another two are not. They are just normal algebra equations but coupled with the differential equation. I wanna use NDSolve to get ...
2
votes
0answers
84 views

Mathematica Newmark Optimization

Here is my Mathematica code which implements the Newmark method to solve a equation of motion. The variable "ag" contains the accelerations from an earthquake record. Is it possible to optimize this ...
6
votes
1answer
132 views

Constrain Locator to specified region

How can I constrain the locator to stay within the region defined by RegionPlot? When the Locator remains within the region, ...
2
votes
2answers
44 views

Numerically solving coupled ODE's with a parameter as initial condition

i'm currently trying to numerically solve a set of coupled ODE's to obtain the functions p(r), h(r) and m(r) in the range of r1 <= r <= r2 with initial conditions m(r1)=a=const and ...
2
votes
1answer
123 views

solving Stokes equations for Force=0 boundary condition

Say you want to solve the movement of a particle in a viscous fluid such that the force on the particle is zero. In general, the solution is trivial since one has no-slip boundary conditions, ie the ...
0
votes
1answer
44 views

Setting Initial Conditions in a System of Differential Equations that don't start at t=0

I have a system of six differential equations (linear for the sake of the discussion). I want to set the initial condition to start at time t=18 and not time t=0. I know the values of the dependent ...
0
votes
0answers
37 views

Extract stiffness matrix from NDSolve

I am solving a set of ODE equations with NDSolve with more than 25 equations. I was wondering is there any way Mathematica gives me the mass and stiffness matrices?
1
vote
1answer
51 views

Finding roots of Bessel function $y=3J_1(x)+xJ_1'(x)$ is returning inaccurate roots. Not Kernel bug [on hold]

I can't figure out why Mathematica is returning the incorrect roots. The first five should be 2.9496,5.84113,8.87273,11,9561, and 15.0624 according to my textbook. ...
2
votes
1answer
62 views

Does NDSolve iterate faster in a region where the system being solved is in equilibrium?

I was wondering how exactly the time it takes for NDSolve to iterate through a certain region of the domain depends on the local behaviour of the given system being solved. My guess would be the ...
0
votes
0answers
40 views

How to speed up NDSolve?

I have a program where I need to iterate NDSolve thousands of times for different configurations of a diffusion problem. The thing is, I only need about 3 digits of accuracy. I looked thru previous ...
0
votes
0answers
44 views

Lyapunov exponent of non-autonomous differential equation

I am trying to calculate the Lyapunov exponent for a non-autonomous system using M Sandri code, but it always shows me error "infinite expression 1/0 encountered". Does anyone know about this? Mr. ...
3
votes
1answer
188 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 ...
13
votes
3answers
489 views

Particles bouncing in a 3D box

I made this Manipulate code which shows a pack of particles randomly moving inside a box. It has a huge performance issue. What should be the best way in doing ...
0
votes
1answer
115 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 ...
10
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
1answer
33 views

Trying to solve ODE. Need help with error messages [on hold]

With this code I get an error-message: Equation or list of equations expected instead of True in the first argument. Apparently y'[0] == v0 gives ...
0
votes
0answers
61 views

Force NDSolve to use finite difference

How to force NDSolve to use finite difference instead of FEM. I have the following code: ...
0
votes
0answers
69 views

Boundary conditions for NDSolve

I get the following message: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> from ...
0
votes
0answers
45 views

Eigenelements of conductivity equation

I am trying to calculate the eigenvalues and eigenfunctions of the conductivity equation in an annulus. In particular I am looking for $(\lambda, u)$ s.t. $$ \begin{cases} \Delta u = \lambda u & ...
0
votes
0answers
39 views

Getting DSolve to return different solutions [on hold]

I am Using 10.0 I am trying to solve the following ODE: $$ \frac{d^2 \psi}{d\theta^2}+ \nu \psi =0$$ , $$\psi(0)=0$$,$$\psi(3\pi/4)=0$$ and Mathematica only sppits out the trivial solution PS: I am ...
10
votes
1answer
193 views

NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
-4
votes
0answers
79 views

Bifurcation diagram for delayed dynamical system [closed]

The delayed dynamical system describe as $\dot{x}(t)=y(t)-ax^3(t)+bx^2(t)-z(t-\tau)+I \\ \dot{y}(t)=c-dx^2(t)-y(t)\\ \dot{z}(t)=r[s(x(t)-e)-z(t)]$ where $a=1.0; b=3.0; c=1.0; d=5.0; r=0.006; s=4.0; ...
0
votes
1answer
33 views
0
votes
0answers
29 views

Solving Time-Dependent PDE's Analytically with no non-trivial Boundary Conditions

I'm having some trouble solving a partial differential equation that is supposed to model the propagation of a scalar field in Schwarzschild spacetime using spherical coordinates. I'm using the DSolve ...
6
votes
0answers
45 views

EventLocator in NDSolve seemingly hogs memory in Windows, but not Mac

I have written a function (ftest in my code) which does the following: Takes a vector {x,vx,vy} as input Numerically solves (with high precision) a specific ...
0
votes
0answers
58 views
0
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0answers
42 views

NDSolve won't stop running [on hold]

I'm trying to solve the wave equation with NDSolve, but everytime I hit evaluate notebook it won't stop running. Any insights? ...
4
votes
1answer
66 views

Issues with modeling pulses in a very simple system of DAEs

Some time ago I had asked this question about evaluation difficulties using Euler Integration to solve a system of ODE where discrete pulses occur. While I have now abandoned Euler integration and ...
0
votes
1answer
61 views

How to perform this nth derivative operation in MMA?

I have to solve this following equation where I need to differentiate a function $n$ times. $$A=\sum_{n=0}^{m-1}\frac{s^n}{n!}(-1)^n\frac{d^nf(s)}{ds^n}$$ How to express the above equation in ...
0
votes
0answers
33 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
1
vote
0answers
75 views

How to “INJECT” with holding Evaluation, specifically into a WhenEvent

I am importing a set of differential and stochastic equations from an external package, and want to use Mathematica to analyse this. I am struggling building the set of equations that I can use with ...
8
votes
1answer
71 views
0
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2answers
82 views

Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
-1
votes
0answers
21 views

How does d/dx (ln(1/x) + c) = d/dx (c - ln(x))? [migrated]

I have to find the derivative of the following expression ln(1/x) + c it appears the answer is -1/x however i am told it can ...
2
votes
1answer
266 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: ...
1
vote
0answers
42 views

Solving ode which solution oscillate violently

This is a ordinary differential equation: y[x]/(-1 + x^4)^2 - ((1 + 2 x^2 + 3 x^4 - 2 x^6) Derivative[1][y][x])/(x - x^5) + Derivative[2][y][x] == 0 I want to ...
0
votes
0answers
27 views

Solving equations but cannot define argument [closed]

Hi everyone I am new to mathematica and I really need help now. The question is like this: I defined a function H(e1,e2) and I want to solve PDEs like ...
1
vote
1answer
199 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
0
votes
0answers
32 views

Pade approximants for Taylor series using mathematica [closed]

fluid-dynamics In running Pade Approximants for taylor series to rationalize using Mathematica for higher degrees, the program gets hanged. What can be the reason ?
3
votes
2answers
89 views

Switching Differential Equation in NDSolve

I am trying to solve the following system of differential equations using NDSolve: $\dot{z}_t=.5(1-z_t)$ $\dot{y}_t=.05y_t+z_t-x_t$ subject to the following constraint: $-y_t-z_t\le0$ where $z_t$ ...
0
votes
0answers
30 views

Pass List / Vector argument through NDSolve to a function

I am trying to pass vector or list as argument to the function from NDsolve.And I am getting these error. Also I am pretty new to stack overflow. Apology if this a possible duplicate. Here is my code. ...
1
vote
1answer
35 views

portions of plot missing for a relatively simple function

I am trying to produce a graph of the linear dynamic system response to a step input. The code is as follows: ...
0
votes
2answers
78 views

Free-fall air resistance problem

I´m working on a free fall problem and I got an equation with variable $k$ when the situation has air resistance. Then I compared with no air resistance equation ($-4.9$, considering t variable). So, ...