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

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71 views

Numericaly solve 3 coupled differential equations [closed]

I'm kinda new to mathematica and I was just trying to solve a system of 3 coupled 2nd order differential equations (for a 3 body under gravitational potential problem simulation). I'm using NDSolve, ...
0
votes
1answer
58 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
0
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0answers
33 views

Series Expansion of Differential Operators [duplicate]

We know about the possibility of series expansion of a function in Mathematica. Same as below, where a function f[a x] is expanded around zero up to 5th order. ...
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0answers
54 views

Orthogonality relations of Hermite polynomials

The Hermite polynomials are orthogonal. $$ \int_{-\infty}^\infty H_m(x) H_n(x) e^{-x^2}\, \mathrm{d}x = \sqrt{ \pi} 2^n n! \delta_{nm} $$ Does Mathematica not use this relationship? Because running ...
0
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1answer
46 views

NDSolve::bcsol?

I'm writing a code to numerically solve a differential equation. It has to repeat the process several times since there is a variable involved which is unknown, and the equation is fit to some ...
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0answers
32 views
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1answer
50 views

Symbolically solve system of equations involving matrix

I need to solve the following system of equations symbolically for a_i, b_i, and c_i: ...
1
vote
1answer
46 views

non linear Least Squares with model function given by ODE's

I have to fit to experimental data a model function given by a linear combination of functions y1(t) and y2(t) a1*y1(t) + a2*y2(t) with a1 and a2 ...
2
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0answers
35 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
19
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1answer
506 views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
2
votes
1answer
129 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
0
votes
2answers
95 views

Using parts of piecewise function

I define: f[x_] := Piecewise[{{5, 0 <= x < 10}, {g[x], 10 <= x < 15}, {h[x], x > 15}}] Then I try to solve ODE: ...
0
votes
2answers
46 views

Manipulating a damped oscillator plot - plot does not show

I was trying to make an oscillation plot that could be manipulated depending on the value of $\beta$. The differential equation is below, and when I just plot the solution, it turns out to be the ...
4
votes
2answers
372 views

Bilateral Laplace Transform

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
2
votes
1answer
56 views

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function?

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function waited to be solved by NDSolve first? For example, ...
7
votes
1answer
142 views

Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
5
votes
0answers
92 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
0answers
21 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
49 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). ...
0
votes
1answer
43 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 ...
0
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0answers
74 views

Plotting a function against some other function?

I want to plot a function against two other functions which are actually determined by ndsolve in my mathematica code. ...
0
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0answers
42 views

BVP Non Linear Shooting Method Implementation

I've been working on this problem for several days. I want to split a 2nd order ode bvp into two auxillary ivps and use those to approximate the solution to the bvp. I have managed to get one ...
6
votes
2answers
471 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from ...
5
votes
2answers
104 views
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0answers
47 views

How to solve using NDSolve

(d^2 f)/(dρ^2 ) + 2/ρ df/dρ = 9 ϕ^2 (f/(1+βf)) Boundary conditions df/dρ=0 at ρ=0 f=1 at ρ=1 We have to make plot of η vs β using following equation with above ...
1
vote
1answer
139 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 ...
6
votes
2answers
238 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 ...
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0answers
67 views

Using Mathematica to solve a recursive system of differential equations

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
35 views

Replacing y[x] with myPowerSeries

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

Coupled Mass Transport in two media using NDSolve

I'm trying to model simple 1-D diffusion in two media with different diffusivities. It's a transient problem so I have a PDE. I have concentration everywhere = 0 at time t=0, and suddenly at t>0, I ...
0
votes
1answer
37 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 ...
1
vote
2answers
182 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 ...
0
votes
1answer
77 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. ...
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0answers
28 views

How to use a While loop with NDSolve?

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

NDSolve with external function

I have a complicated function g[a_,s_,t_] where s_and t_ are constants added by hand for ...
1
vote
2answers
101 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 ...
0
votes
1answer
64 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 ...
0
votes
1answer
43 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 ...
14
votes
2answers
759 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: ...
2
votes
0answers
71 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
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
186 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
167 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
vote
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
votes
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
votes
1answer
59 views

Problem in computing Dsolve

I want to compute my result using Dsolve. The code is given below. ...
0
votes
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 ...