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

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Solving a chemical system using NDSolve

I have to solve a set of coupled differential equations and am not sure how to proceed. It is a model of a chemical process where I'm interested to find the species concentration as $r$ varies. For a ...
4
votes
2answers
119 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} + ...
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0answers
21 views

Solve PDE with DiracDelta function

This question is related to Solve wave equation using DSolve?. I think it is more appropriate to open another question on this topic. In the question, the compatibility conditions can be introduce ...
3
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1answer
115 views
+50

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) = ...
3
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1answer
160 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
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0answers
26 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
0
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2answers
41 views

Setting up two ordinary differential equations [on hold]

Just having a total blank at the moment, I realise that maybe this question would best be suited for a math forum but i assume Mathematica is needed in order to solve these equations. So the question ...
1
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2answers
87 views

How to write absolute value and square root in one equation?(runge kutta) [on hold]

I got some problem when I run my program. It hangs when I run it. This is my coding for runge kutta Geometric mean(RKGM). ...
4
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2answers
3k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
7
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2answers
345 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
19
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2answers
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 ...
1
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1answer
38 views

Trying to find solution for system of ordinary differential Equations [on hold]

I've got 2 functions: A'[t] = (0.5/(1 + (B/k1)^n)) - 0.2*A B'[t] = (1/(1 + (A/k2)^n)) - 2*B with conditions of ...
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1answer
69 views

Diff eqs can be solved?

I'm trying to solve a pair of coupled differential equations, but am having trouble making DSolve evaluate my equations. ...
0
votes
1answer
71 views

nonlinear differential equation

For such a equation $$-y''(x) + x^2\cdot y(x) - |y(x)|^2\cdot y(x) = 0$$ with initial conditions: $y(-500) = 0$ and $y(500) = 0$. I write in mathematica ...
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0answers
53 views

Eigenvalues of the nonlinear Schrödinger equation [on hold]

As an exercise I have to deal with a nonlinear time independent Schrodinger equation eigenvalues and eigenfunction, ...
3
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3answers
89 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
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0answers
72 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 ...
0
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0answers
87 views

Plotting a numerical integration

I have the following code to calculate a numerical integral for any given a: ...
1
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0answers
52 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
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1answer
59 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
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1answer
59 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
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0answers
43 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
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1answer
45 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
69 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
58 views

Problem using NDSolveValue

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

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
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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
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2answers
119 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
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
143 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
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
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0answers
42 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
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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
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0answers
91 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
88 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
59 views

ParametricNDSolve without initial condition?

For example, ParametricNDSolve[{y'[t] == a y[t]}, y, t, {a}] returns a ParametricFunction which is actually inexplicable: ...
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0answers
80 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
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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 ...
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0answers
35 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: ...
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0answers
33 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
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} - ...
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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
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1answer
57 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
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
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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
0
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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
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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 ...