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

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0
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1answer
47 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 ...
0
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0answers
39 views

Eigenvalues of the nonlinear Schrödinger equation

As an exercise I have to deal with a nonlinear time independent Schrodinger equation eigenvalues and eigenfunction, ...
0
votes
1answer
47 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. ...
3
votes
3answers
86 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
33 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} + ...
3
votes
0answers
43 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
46 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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0answers
116 views

ODE fitting to dataset

So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time. ...
1
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1answer
58 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 ...
-2
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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. ...
0
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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 ...
1
vote
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: ...
0
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1answer
55 views

Problem using NDSolveValue

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

Plotting a numerical integration

I have the following code to calculate a numerical integral for any given a: ...
0
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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
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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
votes
2answers
118 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. ...
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
41 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
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
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0answers
78 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 ...
3
votes
1answer
142 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 ...
0
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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
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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: ...
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
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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. ...
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} - ...
1
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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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0answers
32 views

Error when using NDSolve in SIR model

I have the following code for a SIR model: ...
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
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: ...
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?
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 ...
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 ...
-1
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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 ...
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. ...
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, ...
0
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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
45 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). ...
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
1answer
40 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
votes
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 ...
3
votes
2answers
86 views
0
votes
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 ...
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 ...
5
votes
2answers
102 views

Trouble with ParametricNDSolveValue

I have this: ...
6
votes
2answers
237 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 ...