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
153 views

A good choice to find solutions of ODE

In order to rephrase the question. I would ask you to take a look at the following problem: I have this system of ODE: $$ \begin{cases} \dot{x}(t)= x(t)[r_1(t) -b_1(t)x(t- \tau(t)) - c_1(t)y^m(t)] ...
1
vote
1answer
187 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
1
vote
1answer
168 views

Runge-Kutta Butcher tables

I like to have the Butcher's table for Explicit (or implicit as well) Runge-Kutta method of a fixed order. I do not understand reading ...
0
votes
1answer
48 views

Solving a system of ode and plotting the nullclines

I have the following problem to solve it is a system of two ode's. I'm given that q=2/Sqrt[1 + 1600 y] and then the ode's are as follows. ...
1
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1answer
734 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
0
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0answers
50 views

System of non linear differential equations with two unknowns

I am new to Mathematica and am trying to solve a system of 3 (non-linear) equations with two variables $x,\ y$ and one unknown function $f(x,y)$ of these two variables. The third equation defines the ...
0
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1answer
59 views

Problem in computing Dsolve

I want to compute my result using Dsolve. The code is given below. ...
0
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0answers
98 views

Using Runge-Kutta method to find arc length [duplicate]

I don't know much about using the Runge-Kutta method in Mathematica, so I have to ask a straightforward question: How can I use Runge-Kutta to numerically approximate the parameter t of this curve in ...
-1
votes
1answer
91 views

Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
1
vote
1answer
114 views

Why DSolve[] does not work?

I try to find the analytical solution to the ordinary differential equations as fellow: $$\frac{d^2 \theta}{d t^2} = \dfrac{-M\cos\theta\sin\theta(\frac{d\theta}{dt})^2 - ...
1
vote
2answers
92 views

differential equation of order2

I want to solve the following differential equation ode = x*y''[x] + y'[x] + 4*x^2*(x^2 - 1) y[x] == 0 But do not know how to actually solve it. Any suggestion?
0
votes
0answers
95 views

fourier frequency analysis for NDSolve of complex variable

i have a set of coupled equations for complex amplitudes c1 and c2, for which i'd like to find frequency and phases (and phase shift); i looked up for some nswers on the forum, but can't seem to find ...
1
vote
1answer
90 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
9
votes
1answer
640 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
0
votes
0answers
72 views

Black Scholes PDE solved by method of lines

I've been trying to solve the Black Scholes partial differential equation (BSPDE) by transforming it to the heat equation (HE) form and using method of lines (discretizing spatial argument and leaving ...
2
votes
4answers
236 views

Solving differential equation

I want to solve the following differential equation DSolve[y''[x] == (λ y[x])/Sqrt[-1 + x], y[x],x] But do not know how to actually solve it. Any suggestion?
1
vote
1answer
74 views

Solve system of equations with implicit function [closed]

I am trying to solve a system of 3 (non-linear) equations with two variables $x,\ y$ and one unknown function $f(x,y)$ of these two variables. Also, the system includes the change of this function $f$ ...
0
votes
1answer
87 views

Solving differential equation with initial conditions

I want to solve the following differential equation with initial conditions: ...
20
votes
5answers
1k views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
0
votes
1answer
46 views

Solve system of differential equations and show the chaotic behavior of the solutions [closed]

I want to solve a system of differential equations and show the chaotic behavior of the solutions. Here x[t], y[t] and ...
1
vote
2answers
194 views

How to solve for “k”

So the question is given that the atmospheric pressure is modelled by the differential equation p'[h]=-kp[h], p[0]=1013, p[20]=50. find k and comstant of integration. My code was: ...
0
votes
0answers
20 views

ImplicitRegion Error in NDSolve?

I'd like to solve a differential equation with some initial conditions to get an eclipse curve for Earth's orbit using Newton's Law in a cylindrical coordinate. NDSolve gave me two more useless ...
-1
votes
0answers
56 views

CUDA, Fourier and PDE

I am numerically solving by an Runge-Kutta method a partial differential equation of the form $$\frac{\partial}{\partial z} E(z,\omega,r)=\alpha(\omega)FT^{-1}\left[ ...
0
votes
2answers
32 views

solving ode and plotting solution vs time

I'm currently trying to solve this system of two ode's and can't seem to be able to solve them. I am new to coding, so I don't know where I could have done a mistake. I'm attaching the code which I ...
7
votes
1answer
122 views

Difficulty in getting correct Gaussian curve for diffusion of point source

I want to solve diffusion of a point source numerically and check it against analytical solution. first I define initial profile, ...
0
votes
1answer
77 views

My simulation is not never finishing and it is taking so much time?

I am running simple code which involves calculation of two first order differential equations.It is taking so much time and i am unable to get the results as the simulation is never finishing. ...
0
votes
0answers
18 views

How to solve coupled first-order ODE with vectors?

m * v'[t] = q * (E + v x B) using the following: B = (0,0,B0), E=(Eperp,0,Ez). How would I find the general solution of ...
0
votes
0answers
24 views

accessing solution of pde [duplicate]

How can I access the values of solution of a partial differential equation? For example given here, ...
5
votes
1answer
168 views

Numerical solution of IVP for linear ODE with variable coefficient runs wild soon

Cross posted in scicomp.SE. A friend of mine showed me this initial value problem (IVP) for a linear ordinary differential equation (ODE) with variable coefficient: $$y''(x)=\left(x^2-1\right) ...
0
votes
1answer
52 views

DSolve not outputting any result

I'm trying to solve a system of differential equations using DSolve, but I am not getting any output beyond a repetition of my input: ...
-1
votes
2answers
86 views

How to make sure input is an ODE

I'm having trouble wrapping my head around why this isn't an ordinary differential equation. ...
0
votes
1answer
86 views

How To Use D[ ] to Define a System of PDEs

We have two variables $u_{1}$ and $u_{2}$ which are functions of $x,t$. That is, $u_{1}=u_{1}(x,t)$ and $u_{2}=u_{2}(x,t)$. Consider the the system of partial differential equations $$\frac{\partial ...
5
votes
1answer
145 views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
1
vote
1answer
124 views

Solving coupled differential equations with an eigenvalue

I have 2 coupled differential equations with an eigenvalue Ei and want to solve them ...
1
vote
1answer
76 views

Constants from differential equations

I have a problem, I've solved 2 diff equations and I have: ...
0
votes
1answer
53 views

How to properly use conditionals inside NDSolve

Currently I am working with Mathematica to learn the program, and I'm confused what exactly is wrong with this code. ...
2
votes
3answers
595 views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
3answers
101 views

DSolve with assumptions

I'm new to mathematica and was wondering if someone could help me. I have a differential equation which is: $\frac{dy}{dx} = 1/2 y(1 - y)(a - y + a y)$ It has initial condition $y(0) = y0$ and ...
4
votes
3answers
153 views

How to fit parameters in a system of coupled differential equations

Problem description: I'm studying a chemical reaction that can be modeled by a system of coupled differential equations, and I want to use measured data to determine the parameters that appear in the ...
1
vote
3answers
79 views

NDSolve parametric plot

Here is my code. s = NDSolve[{f'''[x] + f[x]*f''[x] == 0, f[0] == A, f'[0] == 0, f'[10] == 1}, f, x] I want to plot f''[0] ...
4
votes
0answers
39 views

Strange behaviour of suggestion bar to solve an ODE, potential bug

InputE^(-(1/2) x[t]^2) (Derivative[1][x][t]^2 - (x^\[Prime]\[Prime])[t]) == 0and evaluate, then press the solve ode button on the suggestion bar. It will return ...
3
votes
0answers
64 views

Diverging solution to coupled second order ODEs from NDSolve

For a physics application I am considering the radial Bogoliubov-de Gennes equations in two dimensions. In dimensionless form they read as follows $$ \begin{cases} ...
1
vote
1answer
102 views

How to combine VectorPlot and Plot3D

I have a problem with VectorPlot and Plot3D, and I have a code for both but I dont know how to plot the same figure. Here is the code for Plot3D: ...
2
votes
0answers
86 views

Creating a nonlinear phase portrait

I am putting all of my code in one block for easy copy and paste. ...
0
votes
0answers
39 views

How to solve a second order non-linear differential equation analytically?

I have the thermoelectric second order non-linear differential equation: Can some one please help me solve this equation. I need to solve for $T$. The two boundary conditions for $T$ are: $\quad ...
0
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1answer
45 views
0
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0answers
34 views

Strange difficulty with DSolveValue

Consider: sys = {u (1 - u + a v), r v (1 - v + b u)} (* {u (1 - u + a v), r (1 + b u - v) v} *) And: ...
1
vote
1answer
46 views

A With and ContourPlot difficulty

Consider: sys = {u (1 - u + a v), r v (1 - v + b u)}; With[{a = 2, b = 3, r = 1}, Evaluate[Thread[sys == {0, 0}]]] Which gives the output: ...
2
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0answers
36 views
6
votes
1answer
99 views

Detecting nearly simultaneous WhenEvents in NDSolve

I am trying to solve a system of (many) coupled nonlinear ODEs. I need to decouple some of the equations (i.e. set the time derivatives of some of the dependent variables to zero) at various points in ...