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

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0answers
29 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 ...
0
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1answer
25 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, ...
2
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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
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1answer
60 views

How to solve in principle such coupled ODEs

One example for coupled ODEs from the Mathemtica help center reads ...
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 ...
3
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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 ...
0
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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 ...
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 ...
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 ...
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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 ...
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 ...
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 ...
0
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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 ...
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,...
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 ...
4
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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: ...
1
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1answer
69 views
0
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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'[...
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. ...
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 ...
2
votes
2answers
65 views
1
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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
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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
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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
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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
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
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 ...
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 ...
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 ...
0
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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: ...
1
vote
1answer
39 views

How to solve DSolve[y'[x] == a Sin[x], y[xo] == 0, y[x], x] [closed]

How to solve with initial value that is parameter y[xo] == 0 DSolve[y'[x] == a Sin[x], y[xo] == 0, y[x], x]
3
votes
4answers
183 views

Coupled linear time-varying system of differential equations. Analytical solution?

How to solve the system analytically in the interval {to,t} ...
3
votes
2answers
81 views

Multiple solutions using the shooting method

I'm trying to solve the above differential equation. I'm using the shooting method, but for each initial guess a different solution appears. Which solution is correct? Is it possible to monitor the ...
0
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0answers
70 views

Selection of plotted graphic (among several) within a manipulate?

I have the following code (looks big but it's quite simple): ...
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
1answer
49 views

Variable name complication with DSolve? [closed]

I'm trying to run the code: ...
2
votes
1answer
64 views

How can I get a list of solution points from NDSolve?

I just need a list of numerical solutions for x[t], x'[t], x''[t]. While I know how to graph ...
2
votes
1answer
126 views

Ito Process paths over a Plot3D

I was wondering if its possible to draw the simulated paths of an Ito diffusion over the probability density function. Ito Process: ...
1
vote
1answer
49 views

Manipulate with DSolve

I have defined a set of differential equations stored in sol and I'd like to plot them while being able to change the parameters. I've tried it like so: ...
2
votes
1answer
71 views

Heat Conduction where thermal diffusivity depends on z

I'd like to know why Mathematica is not solving this problem for me. Let's imagine a body in which the thermal diffusivity varies with z (we have a cyllindrical ...
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 ...
1
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0answers
55 views

Improve speed of RK4 algorithm for solving ODE

For anyone with interests in dynamical system, i'm trying to plot the phase space of a given hamiltonian. My code is this: ...
3
votes
1answer
109 views

failure of code with Helmholtz equation with point source

I am new to the finite elements package in Mathematica. I have a system of equations, one of which is a Helmholtz equation with a point source in the interior of a bounded domain. The following is the ...
1
vote
0answers
35 views

Changing variable in numerical solution

I solved numerically the differential equation: ...