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

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17
votes
1answer
2k views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
0
votes
1answer
35 views

Solving coupled differential equations

I'm trying to solve a pair of coupled differential equations for a spring system, but am having trouble making DSolve evaluate my equations. ...
3
votes
3answers
81 views

Using NDSolve within Manipulate

I'm trying to use NDSolve inside manipulate. Specifically, I have a series of differential equations with coefficients, k1, k2, ...
0
votes
0answers
32 views

Solve wave equation using DSolve?

The wave equation with pined-pined boundary has well-known solutions, but directly input the equation into Mathematica does not return them. $$EI\cfrac{\partial^4 w}{\partial x^4} + ...
0
votes
0answers
70 views

NDSolve and assuming

I am trying to solve the system of PDE with NDSolve and I got an error message like this NDSolve::deqn: "Equation or list of equations expected instead of ...
3
votes
0answers
41 views

How to program efficient undershoot/overshoot

I would like to solve the following boundary value problem for $y(x)$ for a fixed value of $k$ between $0 < k <1$: $$y'' + \frac{3}{x} y' - y + \frac{3}{2}y^2 - \frac{k}{2}y^3=0 \\ y'(0) = ...
1
vote
0answers
113 views

ODE fitting to dataset

So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time. ...
0
votes
0answers
87 views

Plotting a numerical integration

I have the following code to calculate a numerical integral for any given a: ...
1
vote
0answers
45 views

How to incorporate the boundary conditions into the differentiation scheme in MMA?

Let that we want to numerically solve the following PDE \begin{equation}\label{sde} -r V(S,t)+r S \frac{\partial V(S,t)}{\partial S}+0.5 S^2 \text{sigma}^2 \frac{\partial ^2V(S,t)}{\partial ...
1
vote
1answer
57 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 ...
0
votes
1answer
58 views

How I can make the StreamPlot of this differential equation?

I need the StreamPlot of this differential equation but I don't know how. dp/dt=0.4p(1 - p/30), 0 <= t < 5 and 0.4p(1 - p/30) - 0.25p, t > 5
-2
votes
0answers
41 views

system of nonlinear partial differential-algebraic equation [on hold]

I want to solve 2 coupled partial differential algebraic equations. Below is my program. I am not able to find the solution. Please help for the same. ...
1
vote
1answer
44 views

Unexpected behavior of WhenEvent in NDSolve?

In Mathematica 9.0.1, here is a simple code to numerically solve an initial-value problem: ...
0
votes
2answers
68 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
votes
1answer
55 views

Problem using NDSolveValue

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

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
0
votes
0answers
37 views

Defining initial conditions [on hold]

how do I define the initial condition before solving a partial differential equation in order to compare the solution to that of a model?
4
votes
2answers
117 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
votes
2answers
71 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
votes
1answer
139 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
vote
1answer
43 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. ...
0
votes
0answers
40 views

Solving a delay partial differential equation

I am trying to solve the following partial differential equation, $$\frac{\partial\phi[t,x]}{\partial t}=-2\pi\ \delta \ e^{-t}\phi[t,\mu]^{-2} \frac{\partial}{\partial x} \phi[t,x](x-\mu)$$ where ...
1
vote
1answer
223 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 ...
0
votes
0answers
90 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
votes
1answer
87 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
vote
1answer
59 views

ParametricNDSolve without initial condition?

For example, ParametricNDSolve[{y'[t] == a y[t]}, y, t, {a}] returns a ParametricFunction which is actually inexplicable: ...
1
vote
0answers
75 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 ...
0
votes
1answer
88 views

Plotting a NDSolve solution

I'm working on a neutrino oscillations problem, and am running into issues ploting the solution to my differential equations. The equations have non-analytic solutions so I'm using the ...
0
votes
0answers
34 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
vote
0answers
31 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
votes
1answer
50 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} - ...
0
votes
0answers
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
56 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
votes
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. ...
1
vote
0answers
53 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
votes
1answer
45 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 ...
0
votes
0answers
32 views
0
votes
1answer
48 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
45 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
votes
0answers
34 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
votes
1answer
500 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
94 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
43 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
370 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 ...
-1
votes
0answers
36 views

NDSolve second order differential equation with boundary condition [closed]

i have revised my codes several times but i dont get what is wrong. after running it i keep getting dis message ...
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
141 views

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

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...