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

learn more… | top users | synonyms (3)

0
votes
0answers
11 views

ContourPlot using ElementMeshSurfacePlot3D

I would add contours for iso-level values of a FEM solution of a PDE on a generic 3D region; for visualization of values on the boundary I have used ElementMeshSurfacePlot3D of NDSolveFEM Package (as ...
1
vote
0answers
39 views

Partial derivative with Dirac Delta as initial condition

I am trying to reproduce the Faynman-Kac results from this Wikipedia page: Faynman-Kac This is the equation that I am trying to solve: $$ \frac{\partial w(t,x)}{\partial t} = \frac{1}{2} \frac{\...
3
votes
1answer
162 views

NDSolveValue - Heat flux continuity

I'm having some problems with NDSolve and the problem of conduction of heat. Specifically I'm having problems with the continuity of heat flux. First, let me explain what is the physical problem: ...
11
votes
2answers
292 views

Finite difference method not converging to correct steady state or conserving area?

I am working with the following PDE, which is an advection-diffusion type equation. It describes the movement of a fluid-fluid interface inside an annulus of inner radius $R_1$ and outer $R_2$ under ...
1
vote
1answer
76 views

NDSolve solution disagrees with initial conditions

I just solved a differential equation with NDSolve, and the behavior of the solution was not what I was expecting. In trying to track down where things went wrong, I plotted the solution function ...
-5
votes
0answers
74 views

system with MATHEMATICA [on hold]

Can you please help me solve this system of ODEs with Mathematica? f, g, h, ...
2
votes
0answers
55 views

how can i solve non linear ode

How do I solve the following ODE in Mathematica? DSolve[x''[t] + x[t]^2 + x[t] == 0, x[t], t] Such that the answer is as shown: Instead this function gives a <...
1
vote
0answers
27 views

How to define inclusions in FEM/NDSolve?

I am trying to simulate the compaction process of hot mix asphalts and want to do this with mathematica's FEM libraries. How can I define inclusions in meshes (i.e aggregate particles in the binder) ...
3
votes
1answer
82 views

How to solve time dependent pde?

I have set out to try and solve a time dependent wave equation with specific boundary conditions, but I am running into a bit of a snag. As you can see, I am trying to solve for the wave function u[t, ...
4
votes
2answers
149 views

How to find Eigenvalues of Sturm-Liouville problem? Getting wrong Imaginary Eigenvalues [on hold]

I want to find Eigenvalues of following Sturm-Liouville problem D[(2 - MA/κ[s]) q'[s], s] + W Ω^2 q[s] == 0, Where Ω^2 is the ...
0
votes
0answers
77 views

Robust FindRoot search

I have the following simulation that models a rocket landing (flat Earth, no atmosphere, constant gravitational acceleration), which uses root finding to figure out when to start and stop the engines ...
0
votes
0answers
35 views

What is wrong with my formulas for a mathematical model of a double pendulum? [on hold]

I wanted to create a computer simulation on Matlab, using a model for a pendulum from this study (A double pendulum model of tennis strokes. Rod Cross. Uni of Sydney, 2006) - Link I wanted to use the ...
2
votes
0answers
62 views

Interpolating functions and NDSolve

I've been working on trying to get Mathematica to solve this system for a while now, and I have a couple of questions relating to various parts of the system: Interpolating functions: As a number of ...
-5
votes
0answers
19 views

lyapunov versus coupling parameter [migrated]

i need a plot of lyapunov exponent versus coupling parameter graph for lorentz system.using the matlab program i got lyapunov versus time graph using programme below function ...
1
vote
1answer
88 views

Asymptotic solution

I have an ODE V''[z] + ( (I z0^2 w)/(3 (z - z0)^2) + (2 - (4 I z0 w)/9)/(z - z0)) V'[z] + (-(12/41) I z0 w + (23 z0^2 w^2)/369)/(z - z0)^2 V[z] == 0 ...
1
vote
1answer
71 views

How to solve in principle such coupled ODEs

One example for coupled ODEs from the Mathemtica help center reads ...
3
votes
2answers
90 views

Problem using ArcTan inside NDSolve

I'm messing around a bit with using "thrust segments" on a point-mass in NDSolve and have run into a strange problem to do with using ...
0
votes
0answers
24 views

NDSolve: Improperly assigned stepsize

This is not a question which I estimate is aided in answering by providing complete code, which is excessively long. I ran an NDSolve[] at ...
1
vote
1answer
79 views

Substutution of Ansatz of an ODE [duplicate]

I am only beginning to learn to use Mathematica, and got stuck while trying to implement what is apparently a simple substitution rule. So I have a second order ODE in f, and I want to put in the ...
0
votes
0answers
40 views

NDSolve and piecewise functions

I'm trying to use NDSolve on a Pde for a function that is made up of several pretty complicated functions, most of which are themselves functions of an underlying piecewise function. When I try to ...
3
votes
1answer
84 views

Need help understanding the output of `DSolve`

I give Mathematica 10 the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] and I have the following output: ...
0
votes
0answers
3 views

Maximum Likelihood Approach for parameter estimation of multi response data, could you provide a tutorial? [migrated]

I was trying to fit the parameters a time dependent system coupled of ODES relate to a kinetic experiment with multi response data. example: A->B+H A+H->C+H A->D dcA(t)/dt=-k1Ca(t)-k2Ca(t)*Ch(t)-k3*Ca(...
3
votes
1answer
62 views

NDSolve Step Size Effectively Zero

I'm trying to solve a PDE for a function of 2 variables. The most accurate parameterizations of this equation are very unwieldy and involve numerous piecewise elements, and so right now I'm trying to ...
9
votes
1answer
538 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
0
votes
1answer
32 views

NDSolve swapping between solution branches to stay positive

I have a differential equation that I wish to solve, with the requirement that my independent variable must stay positive, but do not require it to remain differentiable. My equation comes from ...
0
votes
0answers
93 views

Need help with very complex mechanical system of equations

I have three equations as follows: $A_p=F \cos(\alpha+ \phi) - \mu N^{'}_{S_1} - \mu N_{S_1} - W \sin \theta = m ( \ddot x - r \ddot \theta (\sin (\gamma+ \phi)) )$ $B_p=F \cos(\alpha+ \phi) - \mu ...
1
vote
1answer
88 views

Getting complex infinity for solution to differential equation

DSolve[y''[x] - (2 n + 1) (3 + 2 n) y[x]/(4 x^2) + \[Beta] y[x]/ x^(-2 n) == 0, y[x], x] I am trying to solve the equation and all I am getting is ...
2
votes
1answer
72 views

How can I find the eigenvalues of a Sturm-Liouville equation?

I am trying to find eigenvalues of a Sturm-Liouville equation using Mathematica10.2, but setting different precisions in ParametricNDSolve gives me different ...
12
votes
1answer
2k views

Solving Killing equations

Is it possible to solve Killing equations in Mathematica for a general vector? I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this. ...
3
votes
2answers
88 views

solving PDE equation like Helmholtz equation in 2D

In my project I need to solve following equation analytically could anyone help me ? As I read the other questions, my equation seems like Helmholtz equation $$ \triangledown^2 u(x,y) - k_cu(x,...
4
votes
1answer
104 views

Mass distribution in NDSolve

I'm trying to model the solar system with NDSolve, basically a numerical n-body solution. I model the initial positions of bodies from a data set thusly: ...
3
votes
1answer
99 views

Getting a function/solution for an ODE over 2 dimensions

I am trying to calculate the laminar flow field within a tubular reactor. The relation between axial velocities, viscosity and pressure drop is given by this differential equation with the axial ...
3
votes
1answer
157 views

Finding eigenvalues for Laplacian operator for 3D shape with Neumann boundary conditions

I've just begun to use the Mathematica so my question may seem to be naive. To get a solution for my problem I looked at the example provided in help. ...
0
votes
1answer
59 views

Coupled differential equation using NDSolve

I am using mathematica to solve a coupled differential equation using NDSOlve and stuck with it. Could you please help me out to figure out the solution. My problem is $$ A[\omega]:= A''[r]+\frac{f'[...
4
votes
1answer
164 views

ColorBars or PlotLegends for ElementMeshSurfacePlot3D

I want to produce a colorbar legend to the output from ElementMeshSurfacePlot3D (Mathematica 10). The pde was solved using NDSolveValue (FEM pdesolution is the resulting interpolating function) over a ...
12
votes
2answers
271 views

Fractal basins of attraction in a Magnetic Pendulum

I am trying to write a Mathematica program that realizes a graphical approximation of the basins of attraction in a Magnetic pendulum subject to friction and gravity, in which the three magnets are ...
4
votes
2answers
249 views

Why Can't `DSolve` Find a Solution for this ODE?

I wanted to find a basis for the set of solutions of the following ODE. $$y^{''}+\frac{1}{x^2+1}y^{'}(x)+\left[-1-\frac{1}{x^2+1}\right]y(x)=0$$ But when I try to use ...
3
votes
2answers
208 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
4
votes
3answers
5k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
1
vote
1answer
71 views

getting a following error,large data points,desired output-best fit to expt. data sets

I am trying to carry out list operation but running into a following error I have large data sets(more than 0.2 million data points) and desired output will be a best fit (numerical data points ) to ...
7
votes
3answers
170 views

Confusion with Neumann and Dirichlet

If I solve Laplace's equation with Neumann boundary conditions then everything is defined via derivatives. Consequently one needs to fix a point with a specific value to get a solution. However if I ...
0
votes
1answer
50 views

How to solve a differential equation system involving complex conjugates?

Consider the following system of differential equations sys = {y'[t] == g*z[t], z'[t] == g*y[t], y[0] == y0, z[0] == z0}; which we can solve ...
0
votes
0answers
14 views

Error witih DSolve [duplicate]

I am trying to solve these differential equations: ...
3
votes
2answers
69 views

How to get value from InterpolatingFunction

I have numerically solved a system of ODEs using NDSolve. I can plot them using ParametricPlot but I am having trouble evaluating them at specific points and ...
0
votes
2answers
59 views

DSolve non linear DE

probably my problem i´m gonna ask seems ridiculous and quite basic. I want to solve an equation with the following code, where a,b,c are parameters. But surprisingly they don´t appear in the solution. ...
3
votes
1answer
99 views

NDSolve DAE solution order is mixed up

Bug in 10.4.0.0, probably introduced earlier. Compare the two solution sets below: in the first one (x == False), there are only 3 dependent variables while in ...