Tagged Questions

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

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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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?
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. ...
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 ...
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 ...
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. ...
1answer
188 views

1answer
66 views

How do I extract the values returned as Root[,] after solving the Sturm Liouville problem to take the square root?

$y''+\lambda y=0, y'(0)=0,y(1)+y'(1)=0$ ...
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 ...
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 ...
0answers
79 views