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

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0
votes
2answers
28 views

Plotting direction fields along with trajectories

I am reading "Dynamics and Bifurcations" by Hale and Kocac, and in chapter one the following diagram is shown: Question is, how can I achieve the same plot using Mathematica? I've tried ...
0
votes
1answer
35 views

Encountered non-numerical value for a derivative at x==0 [on hold]

this may be a duplicate question but I still don't understand how to get around this problem after reading through other posts. I'm trying to solve a differential equation ...
5
votes
0answers
42 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
-2
votes
0answers
37 views

Nonlinear eigenvalue problem

I deal with such a equation $$-y''(x) + x^2\cdot y(x) - |y(x)|^2\cdot y(x) = E y(x)$$ where E is eigenvalues with initial conditions: $y(-300) = 0$ and $y(300) = 0$. I want to figure out ...
1
vote
0answers
30 views

Using an arbitrary area bounded by lines for PDEs?

I have a set of lines I pulled from an image that make a closed loop, pretend it's a unit square for reference. Is there a way to use such an arbitrary region for solving PDEs, and is there a way to ...
0
votes
2answers
42 views

Plotting a Forced Vibration Differential Equation [on hold]

I'm attempting to plot a differential equation solution but mathematica is giving me trouble. The plot is showing up blank. Here is what I have. ...
0
votes
0answers
28 views
4
votes
1answer
107 views

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 ...
1
vote
0answers
53 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 ...
1
vote
0answers
53 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
votes
2answers
59 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
vote
2answers
92 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). ...
1
vote
1answer
52 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 ...
0
votes
1answer
79 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
votes
0answers
60 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, ...
1
vote
1answer
74 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
92 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, ...
5
votes
2answers
176 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} + ...
4
votes
1answer
138 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) = ...
1
vote
0answers
57 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 ...
3
votes
1answer
171 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
vote
1answer
60 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
votes
0answers
43 views

system of nonlinear partial differential-algebraic equation [closed]

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
108 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
46 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
1answer
63 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
votes
2answers
71 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
0answers
37 views

Defining initial conditions [closed]

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
123 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
vote
1answer
44 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
44 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
60 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
85 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
157 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
votes
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: ...
1
vote
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
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
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. ...
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
vote
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
votes
0answers
33 views

Error when using NDSolve in SIR model

I have the following code for a SIR model: ...
0
votes
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 ...
0
votes
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: ...
2
votes
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?
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 ...
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 ...
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. ...
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, ...