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

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0
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1answer
24 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, ...
0
votes
0answers
28 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
44 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
86 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
60 views

How to solve in principle such coupled ODEs

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

How to find Eigenvalues of Sturm-Liouville problem? Getting wrong Imaginary Eigenvalues

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 ...
3
votes
2answers
84 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
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0answers
22 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
75 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
36 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
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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
57 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
31 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
92 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
85 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
70 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
87 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
102 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
98 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
2answers
153 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
265 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 ...
3
votes
1answer
135 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: ...
7
votes
3answers
166 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
49 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 ...
8
votes
2answers
271 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 ...
0
votes
1answer
49 views

a question about singularity in numerical calculation

Suppose I want to numerically calculate a PDE as following $$a\frac{\partial^2}{\partial x^2}f(x)+\frac{b}{x}\frac{\partial }{\partial x}f(x)+c=0, x\in (-1, 1)$$ where $a$, $b$, $c$ are constants. So ...
3
votes
4answers
183 views
0
votes
1answer
82 views

Need Help to solve a ordinary differential equation

I need help to find a solution to the differential equation bellow. The solution obtained with this code is a very small negative number in all the domain, and it was mathematically proved that exists ...
21
votes
2answers
1k views

1D Euler equations (fluid dynamics) with NDSolve

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the problem given here: http://www.csun.edu/~...
3
votes
1answer
54 views

How to index multi-dimensional vectors in NDSolve/WhenEvent?

I want to solve a system of coupled ODEs using NDSolve with WhenEvent. But I'm having a hard time trying to index the state ...
0
votes
1answer
143 views

Result interpretation of a general solution of a nonlinear differential equation

My goal is to find the general solution of the following nonlinear differential equation: $$x'(t) = e^{-t} - \sqrt{x(t)}$$ Following this guide, I've entered in the Wolfram Mathematica the following ...
0
votes
0answers
89 views

Help numerically solve this non-linear PDE with singularity

I have trouble finding a numerical solution to the partial differential equation below. It seems to be a singularity in the solution somewhere, so I searched online and found that it is suggested to ...
3
votes
1answer
123 views

Finding Maximum Value of ElectricField in a bounded region

I have been trying to find the maximum value of the magnitude of an electric field in a bounded region. NDSolve gives the value of the potential inside the region ...
0
votes
0answers
34 views

How to solve coupled diffrential equation in closed form [duplicate]

How to solve the system analytically in the interval {to,t} x''[t]==-a0*(a1 - b*z'[t])*Cos[w*t] z''[t]=-a0*b*x'[t]*Cos[w*t] This gives an error: ...