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

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0answers
79 views

Working with vector-valued functions to solve an ODE

Let's say I have a simple vector-valued ODE given by $y'(t) = K*y(t)$ where K is a matrix $K_{n_{X}n}$. Let's assume that the matrix is $K_{21_{X}21}$, $K = \left[\begin{array}{cccc} k_{1_{X}1} ...
0
votes
1answer
336 views

How to plot trajectory for a differential equation in polar coordinates? [duplicate]

I have a differential equation for dr/dt and d[Theta]/dt in terms of r and theta, and I am trying to plot the trajectory in the x-y plane for a given initial condition (r,theta). ...
6
votes
1answer
201 views

NDSolve computes wrong solution?

Please excuse me if the question has already been answered somewhere else, but I was not able to find it. Could somebody tell me what I am doing wrong here? The solution of DSolve is of course correct ...
0
votes
1answer
109 views

Orthogonal Collocation Using Jacobi Polynomials

I'm trying to solve a PDE(diffusion-reaction in a spherical catalyst pellet) using Jacobi Orthogonal Collocation method. But at the stage of solving the system of ODEs(using ...
3
votes
2answers
136 views

How to extract state vector after NDSolve for subsequent re-use?

I'm using code like this: ...
5
votes
2answers
176 views

Trouble with ParametricNDSolveValue

I have this: ...
6
votes
2answers
341 views

Using NDSolve to produce 10,000 points of a solution

I am beginning to read the Differential Equations Laboratory Workbook by Borelli and the preface begins with an image. I understand how to use NDSolveValue (at a ...
0
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1answer
39 views

Replacing y[x] with myPowerSeries

Consider: myPowerSeries = Series[y[x], {x, 0, 3}] Which produces this output. ...
1
vote
0answers
119 views

Using Mathematica to solve a recursive system of differential equations [closed]

I believe I have a difficult problem to work on specially because I don't have any previously experience using Mathematica in this kind of situation. So I'll try to describe it as best as I can hoping ...
0
votes
1answer
98 views

Having trouble interpreting the results DSolve gives for the Laguerre equation

I am trying to solve a second order ODE using Mathematica. Before I get into solving my (more complicated) problem, I am trying to use DSolve on known ODEs to check that the answer that Mathematica ...
0
votes
0answers
89 views

How to use a While loop with NDSolve?

So basically I have this coupled ODE system I'm trying to solve numerically: ...
1
vote
0answers
39 views

NDSolve with external function [closed]

I have a complicated function g[a_,s_,t_] where s_and t_ are constants added by hand for ...
1
vote
2answers
338 views

How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
1
vote
1answer
211 views

Solution of a system of differential equations with a correction factor varying over time

Dear Mathematica users, I am trying to solve a system of equations of first order and time depedent. The system has 5 equations, one for every variable which varies over time. At the moment I am ...
0
votes
1answer
59 views

simple dynamical system with disturbance

I am new here and trying to simulate a very simple dynamical system with periodic force or Dirac function: $$mx'' + bx' + kx = u(t)$$ I want to draw the displacement(position) and velocity of the ...
0
votes
1answer
92 views

Why does DSolve not give the expected analytical solution for a system of DAE? [closed]

I made a mistake in typo I am trying to solve the following system of DAE: X'[t] - y*Y[t] + x*X[t] == 0 Z'[t] - y*Y[t] + x*Z[t] == 0 X[t] + Y[t] + Z[t] == 1 with ...
3
votes
0answers
323 views

Problem solving a nonlinear partial differential diffusion equation [closed]

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
0
votes
1answer
121 views

How to compute DSolve or NDSolve for kind of piece wise function?

I need to Compute the expression for two functions. q[t] and q1[t] over certain range of time. The code is given below. ...
0
votes
1answer
253 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
vote
2answers
122 views

Minimize the sum-of-squares errors for a system of ODEs

I'm trying to minimizing the sum of squared errors on a 2-equation system of ODEs and empirical data. I keep getting an error and I think the root of the problem is my invocation of ...
1
vote
1answer
469 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 - ...
0
votes
1answer
67 views

Problem in computing Dsolve

I want to compute my result using Dsolve. The code is given below. ...
1
vote
0answers
182 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 ...
1
vote
2answers
112 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
84 views

DifferentialRoot

I want to obtain y(x) of following answer with Mathematica: and my code is ...
1
vote
1answer
278 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 $f$ ...
15
votes
1answer
1k views

Solving and Animating Three Body Problem

I am attempting to solve a three-body problem using the Lagrange formalism, with a 1/r potential. I started off by defining T and U (kinetic and potential energy) as follows: ...
0
votes
1answer
61 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 ...
0
votes
2answers
216 views

Solving differential equation with initial conditions

I want to solve the following differential equation with initial conditions: ...
-1
votes
1answer
110 views

Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
1
vote
2answers
236 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
2answers
47 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 ...
0
votes
1answer
91 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. ...
7
votes
1answer
194 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
0answers
38 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
1answer
100 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
1answer
95 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
254 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 ...
8
votes
1answer
909 views

Animated Wave propagation using split operator method

Here is the state of the art: By solving the time-dependent Schrödinger equation, one obtains that the propagated wave function after time step $\Delta t$ can be calculated by applying the ...
5
votes
1answer
525 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
205 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. ...
1
vote
1answer
93 views

Constants from differential equations

I have a problem, I've solved 2 diff equations and I have: ...
2
votes
3answers
719 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
299 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
117 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] ...
5
votes
1answer
405 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) ...
4
votes
0answers
49 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 ...
8
votes
1answer
363 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
168 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: ...