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

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1answer
83 views

Power::infy: “Infinite expression 1/0. encountered” (ODE Solution using NDSolve)

While solving the following ode, Eq1 = f'''[x] - f'[x]*f'[x] + f[x]*f''[x] - K1*(2 f'[x]* f'''[x] - f[x]* f''''[x] - f''[x]*f''[x]) - f'[x] == 0 with the ...
1
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1answer
48 views

Unexpected behavior of WhenEvent in NDSolve?

In Mathematica 9.0.1, here is a simple code to numerically solve an initial-value problem: ...
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2answers
82 views

Plot ParametricNDSolve

I am trying to plot the probability of a molecule being in a certain state via the numerical solution of the Schrödinger's equation of molecule in an oscillating electric field (in a rotating system). ...
0
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1answer
71 views

Problem using NDSolveValue

Good afternoon, fellas. Could anyone here help me solve this problem? ...
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0answers
75 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
4
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2answers
155 views

Evaluation problems with NDSolve using the fixed step ExplicitEuler-Method

Motivation I am using Mathematica to implement System Dynamics (SD) models, e.g. differential equation models as applied to management/economic problems following the "methodology" of Jay W. ...
0
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2answers
72 views

Integrating ODE's

I have: $$ m\frac{dV_y}{dt}=-k\cdot V_y-mg $$ where, $V_y$ is velocity in the $y$-direction. I have the initial condition Vy[0]=40 Sin[40 Degrees] and ...
3
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1answer
163 views

Adding noise to nonlinear ODE system

I have a problem with adding a noise to 3d order ODE nonlinear system. I solved the system numericaly and got the periodic solution and now I need to add random pertubations. Due to the lack of ...
1
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1answer
46 views

Solving ODE having function which changes conditionally

I want to solve the following set of ODE with a piecewise function A[t] which changes if a certain condition is satisfied. ...
1
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1answer
246 views

Partial differential equation with initial conditions

And so I want to solve the following equation, subject to these initial conditions: $\ u_{tt} - u_{xx} = 6u^5+(8+4a)u^3-(2+4a)u$ $\ u(0,x)=\tanh(x), u_t(0,x)=0$ When I use NDSolve to solve within ...
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0answers
106 views

Heat Equation with Neumann Boundary Conditions and Lateral Heat Loss

I am trying to solve the following heat equation with Neumann BC's: $\quad \quad u_t$=$\alpha ^2$$u_{xx}$-$\beta$ (u-$T_0$) $\quad \quad u(x,0)=f(x)$ $\quad \quad u(0,t)_x=0$ $\quad \quad ...
2
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1answer
99 views

How to write ODE to standard form?

Package like odepack needs the ODE written in standard form, which means write the high order ODE to first order ODE equations. The steps of converting ODE to ...
1
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1answer
68 views

ParametricNDSolve without initial condition?

For example, ParametricNDSolve[{y'[t] == a y[t]}, y, t, {a}] returns a ParametricFunction which is actually inexplicable: ...
2
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0answers
117 views

Choosing FEM element type and mesh refinement

I have only recently been introduced to Mathematica's(v10.0) FEM capabilities. I understand that for solving PDEs on non-uniform shapes via NDSolve, Mathematica ...
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0answers
38 views

Differential equations: Solving a PDE

I need to find an analytic solution to this PDE and for some reason nothing works. This is the equation: ...
1
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0answers
42 views

Solving non-linear coupled ODE with constraint using NDSolve

I am trying to use NDSolve in Mathematica to solve the following coupled ODEs from a paper I am trying to understand. I have the following 5 differential equations: ...
2
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1answer
56 views

Plot directional field with a initial vlue

I do not have enough reputation to comment on other questions, hence I have to ask my own one I want to solve the following nonlinear first order ODE, $$(1 + x) (0.5 y[x]^{-0.5} (x - y[x])^{0.5} - ...
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0answers
36 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
59 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
52 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
37 views
0
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1answer
56 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: ...
2
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0answers
48 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?
20
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1answer
587 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. ...
0
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2answers
99 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: ...
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2answers
49 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
395 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
60 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, ...
8
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1answer
151 views

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

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
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0answers
108 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 ...
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0answers
25 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
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1answer
67 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
59 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
76 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. ...
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0answers
54 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
477 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
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2answers
115 views
0
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0answers
52 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
145 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
258 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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0answers
74 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
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1answer
36 views

Replacing y[x] with myPowerSeries

Consider: myPowerSeries = Series[y[x], {x, 0, 3}] Which produces this output. ...
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0answers
26 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
42 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
212 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
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1answer
87 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
33 views

How to use a While loop with NDSolve?

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

NDSolve with external function

I have a complicated function g[a_,s_,t_] where s_and t_ are constants added by hand for ...