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

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-2
votes
0answers
56 views

Shooting method [on hold]

can someone look at my equations http://imagebin.org/306581 , and tell me how would I simulate it? Any idea would work. I am looking for a start. I have a code in matlab, but its taking vary long, and ...
2
votes
0answers
50 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
2
votes
1answer
110 views

Different Poincaré maps for same Equation

I've seen the Wolfram Poincaré example. I'd like to modify this sample in order to have a list of Poincaré maps. In the example the event is captured only when ...
0
votes
0answers
45 views

Automatic method for NDSolve [duplicate]

How can I understand which method Mathematica automatically chooses to use for numerically solving the following two equations? 1: ...
0
votes
0answers
80 views

Calculating the Lyapunov Exponent/Spectrum for the Duffing Oscillator

Some fellow students and I are trying to calculate and plot the Lyapunov spectrum for the Duffing oscillator (currently a test approach). Each of us has Mathematica knowledge based purely on past ...
0
votes
0answers
48 views

Solving Laplace-Beltrami Equation on a Curved Surface [on hold]

Suppose that we have a curved surface $S$, specifically, $S$ is a bump, i.e., $x=\rho\cos(\theta)$, $y=\rho\sin(\theta)$, $z=h\cos^2(\frac{\pi\rho}{2R})$, where $\rho$ runs from $-R$ to $R$ and ...
0
votes
1answer
44 views

Dsolve is not solving equation ( 3 system with 2.order diferantial equations) [on hold]

I added an image of my equations at the bottom. I dont understand why it is not solving. This is 3 systems with 2.order diferantial equations. I also put my initial conditions. But it is not solving. ...
0
votes
1answer
68 views

Solving System of Nonlinear with Three Differential Equations

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
1
vote
1answer
91 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
0
votes
0answers
47 views

Derive a PDE from other PDEs

I'm trying to do some symbolic calculation like this: Substitute (11.2) into the last two of equations (11.1) and, in turn, substitute these into the first of equations(11.1), I want to ...
0
votes
0answers
35 views

Why isn't Mathematica plotting my differential equations? [closed]

So here are my equations eqns = {x'[t] == a*y[t] - b*x[t] + g, y'[t] == c*x[t] - d*y[t] + m, x[0] == 60937, y[0] == 13797}; Then I solved it with ...
0
votes
0answers
48 views

How to solve Stokes equations with non-vanishing boundary condition on two spheres? [closed]

I want to solve the Stokes equations for two spherical bodies (some distance apart) with prescribed velocity on their surfaces, in an otherwise static fluid ($\mu$ and $p$ are constants) $$ \left\{ ...
0
votes
0answers
23 views

What is the function derivative [closed]

What is the function derivative? f'(x)=? what is the way to the answer?
0
votes
0answers
46 views

NDSolve: Couple ODE and PDE

I am trying to numerically solve an equation with NDSolve, where there is a ODE coupled to a PDE, like the following: ...
0
votes
1answer
72 views

How to work with Interpolating Function?

I'm starting using Mathematica. I have two coupled differential equations and after using NDSolve the output is in the form of a Interpolating Function. I want to Plot the square modulus of one of the ...
0
votes
0answers
43 views

DSolve failing to solve second-order ODE with two boundary conditons [closed]

I am utilizing Mathematica to solve the following equation: $$y^{''}(x)-5y^{'}(x)+10y(x)=10x $$ The following stated boundary conditions are supplied: $$y(0)=0 \ \ y(1)=100 $$ The following error ...
0
votes
1answer
54 views

Unable to configure a system of differential equations

My differential equations have been written as ...
0
votes
1answer
97 views

I don't understand ListCorrelate! [closed]

I want to solve a PDE equation (like Schrodinger equation) using finite difference in Mathematica. I don't understand what this code does! ...
0
votes
1answer
99 views

predator prey model with prey refuge

I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator.And this is the system $x'=\alpha ...
0
votes
0answers
30 views

Multivariable Delay Diff. Equ. with Ndsolve and Nintegrate

I'm trying to simulate the following equation in Mathematica for $u(x,t)$: $$\frac{1}{\alpha} \frac{\partial u(x,t)}{\partial t} = -u + \int_{-\infty}^\infty {\rm d} y w(y) f(u(x-y,t - |y|/v))$$ ...
4
votes
1answer
114 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
0
votes
2answers
75 views

Constraining function found by NDSolve to stay positive

I am trying to constrain my variables in NDSolve so that they stay positive for the integration interval. Is is possible to do that? Using Assumptions as in ...
0
votes
0answers
44 views

Fit a 2 variable ODE to data and estimate parameters [closed]

I am trying fitting on mathematica for the first time. I can do the one variable ones using the sample code. But here I cannot. Can someone help me fit to the data to get answers. I am trying to fit ...
-1
votes
0answers
41 views

Numerical solution of an ODE with a singularity at the initial value

I have a differential equation: (c^2-y[x]^2)*y'[x] - (a+b)*y[x]^2 + ((2/x)*c^2)*y[x] - c^2*b = 0 with the initial condition ...
0
votes
0answers
54 views

Solving systems of equations and derivatives

I am new to Mathematica, and I'm not sure how to solve a system of equations that include differentiation. Given that f and g are differentiable functions: ...
1
vote
1answer
72 views

Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
0
votes
1answer
59 views

Problem with Plot and ParametricNDSolve

This is my first question on this site, I hope it is written in an understandable way. Let's start. My aim is to plot a certain parametric region, with $x$ and $y$ coordinates given by the following ...
3
votes
1answer
229 views

Solving a differential equation with initial conditions

I want to get a solution to an ordinary differential equation with imposed initial conditions. I'm confused about why my following code doesn't work: ...
1
vote
1answer
63 views

Non-numerical value for a derivative on NDSolve function

I am trying to solve the following system of differential equations: ...
0
votes
1answer
78 views

DSolve does not give solution

No answer is given when I evaluate the following expression: ...
1
vote
0answers
89 views

Runge-Kutta-2 on System

After spending some time using the Mathematica documentation and this Mathematica.SE answer, I implemented the Runge-Kutta-2 routines. I am hoping someone can validate what I did and tell me that it ...
1
vote
1answer
85 views

Solution of an ODE in implicit form

For some non-linear ODEs there is only implicit form of solution using DSolve. For example DSolve[(y[x] + x - 1)*y'[x] - y[x] + 2 x + 3 == 0, y[x], x] gives ...
3
votes
1answer
86 views

Polar Differential Equation

I have a polar differential equation (this is the reduced variant) as: $$r' = 0, \theta' = 1$$ I figured out (from previous answers) that I can nicely convert this to Cartesian and use StreamPlot ...
1
vote
1answer
56 views

Variable location for intial value in ParametericNDSolve

I am trying to figure out if Mathematica allows a variable location for a known initial value for ParametricNDSolve. I haven't been able to find an example where ...
2
votes
0answers
51 views

Locate Blow-up in NDSolve with Whenevent

At some point I get this error: ...
0
votes
0answers
24 views

fitting system of ODEs - “part2 of {} does not exist” errod

I'm trying to fit my data to a system of ODEs: x'[t]==a*x[t]+b*y[t] y'[t]==c*y[t]+d*x[t]+e*z[t] z'[t]==f*z[t]+g*y[t] having t,x[t],y[t],z[t]. I followed the code ...
0
votes
0answers
20 views

How do you find the general solution to a higher order nonhomogeneous differential equation? [migrated]

Find the general solution: y'''-3y''+3y'-y=t*exp(t) <-3rd Order y''''-2y'''+2y''=t*exp(t)*cos(t) <-4th Order
0
votes
1answer
57 views

NDSolve accuracy related problem

I want to solve this equation: ...
1
vote
0answers
58 views

BVP system of nonlinear coupled ODEs

Here I am, trying to solve this system of coupled ODEs (up to a minus sign): $ u''=6u^5-(8+4a)u^3+(2+4a)u+\frac{2u((w^2-s)^2+bw)}{(u^2+c)^2}$ $ w''=\frac{4w^3-4bw+b}{u^2+c}$ with the boundary ...
0
votes
1answer
43 views

Discrete sampling of interpolating function returned by NDSolve

When solving an ODE with NDSolve, Mathematica returns an interpolation function. I need a discrete sampling of this function however. Naively, I can write this as (example): ...
0
votes
1answer
82 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
3
votes
1answer
146 views
0
votes
1answer
154 views

Heat Transfer equation by numerical methods

I want to solve the following heat conduction equation using numerical methods: D[u[x, t], t] -alpha*D[u[x, t], {x, 2}] == 0 u[x, 0] == 1/(1 + x^2)^0.25, u[-10, t] == u[10, t] == 0, ...
-2
votes
0answers
47 views

periodicity of a solution of ndsolve pde

I am solving a pde with NDSolve and the solution is like U(x,t) which seems to be periodic and I am trying to find an algorithm to find the periodicity of such numerical solution. my code is like ...
1
vote
0answers
30 views

How to find discretezation error of NDSolve

Is there a way to find out how large the truncation, round-off, and other errors that occur from discretizing a differential equation are while using the default settings in NDSolve? Or would I have ...
2
votes
1answer
100 views

Trying to solve a differential equation with a piecewise initial condition

I am trying to solve $$u_t=\frac{1}{4}u_{xx}$$ $-\infty<x<\infty,\: t>0$ With the initial condition $u(x,0)=\phi(x)$ where $$ \phi(x)= \left\{ \begin{array}{lr} 1 & ...
1
vote
0answers
58 views

ExpToTrig transforms solution to 4th order ODE into unwanted form

Mathematica gives the solution of the second order differential equation DSolve[a y''[x] + b*y[x] == 0, y[x], x] in trigonometric form ...
-2
votes
2answers
89 views

How do we solve third order nonlinear differential equation f’’’+ff’-f’2-Re2 f’=0

How do we solve third order nonlinear differential equation f’’’+ff’-f’2-Re2 f’=0 f(0)=0,f'(0)=1,f(Infinity)=0 From the OP's comment: ...
0
votes
0answers
49 views

Simplify DSolve solutions (all roots are known)

I have problem how to present the solution of the system of two differential equations in the form as in the case of one differential equation if I know the nature of roots. For example ...
0
votes
1answer
89 views

NDSolve in exact points - nonlinear equation (Degrees and Radians confusion)

I found solutions of two nonlinear equations, but I have three small questions. First I am in confusion because of initial value. The system is mechanical and unknown ϕ is an angle, which I set to ...