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

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4
votes
2answers
143 views

Solving parametric ODEs at large parameter values

Question 101668 was not particularly clear and was put on hold for that reason. The author did clarify it a bit, but it seems unlikely that the question will be reopened. Through an exchange of ...
0
votes
2answers
149 views

How can I perform NIntegrate with NDSolve?

I'm a new user and I have no idea how to perform NIntegrate by using NDSolve. For example consider following differential equation (DE): ...
1
vote
0answers
97 views

Problem setting boundary conditions with NDSolve [closed]

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu ...
1
vote
1answer
56 views

Getting Data from Differential Equation Solution

I am solving the following differential equation. I need to get the values of y[x] for x ranging from 1 to 30. I need to get ...
0
votes
1answer
60 views

Shooting method — why is NDSolve giving me an error message?

I am currently trying to write a code to implement the so-called shooting method (I've given a brief description of it below, for those unfamiliar) for second order ODE's in the form ...
1
vote
1answer
141 views

Why can DSolve not solve this ODE? [closed]

I wish to solve an equation for the field lines of an electric field. This is the textbook question 1.3.8(a) from D. Dubin's Numerical and Analytical Methods for Scientists and Engineers, Using ...
2
votes
1answer
166 views

How to solve $x' = A\cdot x$? [closed]

I want to solve this equation x' = A x in which x' is a 1*18, ...
4
votes
1answer
111 views

StreamPoints adding extra information

Why doesn't the red line start precisely at the defined point $(0, 2)$ and go off to infinity? My initial condition is $(0, 2)$ and I only want to see where that trajectory goes off to. ...
0
votes
1answer
57 views

How can I solve NDSolve with a parameter?

I'm a new user and I have no idea how to solve the equation with a parameter by using NDSolve. For example consider following differential equation (DE): ...
0
votes
0answers
42 views
4
votes
1answer
82 views

DSolve returning InverseFunction while I believe the answer isn't so complicated

I was trying to solve the following differential equation: $$A'(y)^2 = -\frac{1}{l^2} e^{-2A(y)} + \frac{1}{L^2}.$$ I know that one possible answer is $$A(y) = \log\left( ...
2
votes
1answer
82 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
1
vote
1answer
74 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by ...
0
votes
3answers
168 views

About a simple differential equation

Just a simple differential equation.Even we can hand to solve it.But the Mathematica give a error. ...
2
votes
1answer
132 views

Solve 2D diffusion equation in polar coordinates

I am trying to solve the diffusion equation in polar coordinates: $\frac{\partial u}{\partial t} = D \left( \frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r}\right)$ ...
0
votes
1answer
109 views

Mathematica 10.3 Dsolve solving a simple PDE [closed]

I tried to use Mathematica 10.2 and 10.3 to solve this simple PDE and I want to a general solution. But it seems not working. DSolve has been improved in v10.3. But we see it's perhaps not improved ...
2
votes
0answers
88 views

Bypassing a Singularity

I am having trouble trying to solve an ODE that has a singularity when the function M[x]=1. Basically the denominator has ...
0
votes
0answers
96 views

basin of attraction in 3D

I am trying to find a basin of attraction for a 3 dimensional ODE. I am not sure why it isn't working since it worked great for the 2D case. Any help would be much appreciated. My attempt: ...
11
votes
4answers
395 views

periodic boundary conditions and NDEigensystem

Mathematica 10 has a splendid new function, NDEigensystem, that makes it possible to solve Sturm-Liouville problems numerically in a single step. I have not however been able to find a way to get it ...
4
votes
1answer
323 views

Mathematica 10.3 Dsolve solving 2D diffusion PDE

I tried to use Mathematica 10.3 DSolve to solve 2D diffusion PDE with Dirichlet boundary conditions. But it seems not working. Could anyone help check the code? ...
1
vote
0answers
77 views
1
vote
2answers
71 views

NDSolve with one parameter

This is a copyable minimal example to illustrate the problem that occours when I include one parameter U into a differential equation which I want to solve with ...
0
votes
0answers
83 views

How to simplify a messy integrand by integrating by parts

I have a function x[t] and a messy integral over t, containing x[t], ...
0
votes
0answers
63 views

Boundary Value Problem - boundary conditions aren't being met.. HELP?

All, I am trying to solve a system of 4th order differential equations with boundary conditions. Without defining any precision, the resulting solutions do not agree with the boundary conditions. ...
0
votes
1answer
102 views

Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
5
votes
0answers
74 views

Error with DSolve

I am trying to solve the following partial differential equation for the function $f(x,y,z)$ $\frac{(\alpha -\beta y)}{1-y^2}\left(\frac{\partial f}{\partial x} + \frac{(\alpha y-\beta ) ...
0
votes
0answers
37 views

Why does NDSolve and ParametricNDSolveValue show different memory manage in same loop?

This is a follow-up question about How to delete InterpolationFunction created by NDSolve/ParametricNDSolve?. In the previous question, J. M.♦ and Albert Retey showed $HistoryLength = 0 and Clear[] ...
0
votes
2answers
46 views

Plot Piecewise does not work with NDSolve, works with ordinary function [closed]

How to join output from NDSolve with another function in a plot, using Piecewise or something else? I could join a simple function with another in a plot, but could not do it for the output. MWE: ...
1
vote
0answers
50 views

Eliminate a variable from a differential equation and an algebra equation then collect the remaining variables

Recently, I am attempting to eliminate a variable from a differential equation (DE) and an algebra equation (AE), then collect the remaining variables as a new (grand) parameter. Actually, I have ...
0
votes
1answer
120 views

Plotting two variables indirectly dependent on each other

I have the following system of linear ODEs for "i" number of species "c" migrating in "j" number of habitats: ...
1
vote
1answer
130 views

Time-dependent pde with periodic boundary conditions - NDSolve gives incorrect results

I'm trying to solve very simple differential equation with perdiodic boundary conditions and non-constant initial condition, however the results I'm getting don't seem to be correct. Here's my code: ...
1
vote
1answer
92 views

Plotting data from a Table in Mathematica

I have been able to solve some differential equations using Tables. The code works fine without errors. However, I am unable to plot the results. Any help would be appreciated. ...
2
votes
1answer
125 views

NDSolve::depdole error

I'm trying to solve a pair of differential equations with NDSolve. They contain a discontinuous function bounce. I've trimmed ...
3
votes
1answer
177 views

How to work with ParametricNDSolve?

Update 3: I got it. A small dumb mistake... It has to be Evaluate[xP[y]'[0] /. s10] like this. Oh well... Update 2: So if do this ...
0
votes
0answers
133 views

Three Body Problem Equilateral Triangle

I'm currently working on showing that the equilateral triangle arrangement of the three-body problem has an analytic solution. So far I've written the equations of motion of each body into Mathematica ...
1
vote
1answer
101 views

Boundary conditions shooting method

I am trying to solve the differential equation $\frac{d^{2}y}{dr^2}+(\frac{1}{r}+1)y=0$ with the boundary conditions $y(r) \rightarrow r \frac{dy}{dr}(0)$ as $r \rightarrow 0$ and $y(r) \rightarrow ...
3
votes
1answer
99 views

Kernel crash when evaluating NDSolveValue

I had a code that was working fine and I tried to add an extra few lines to find the solution of the same equation with different conditions. The original NDSolveValue solutions work fine but when it ...
-1
votes
1answer
170 views

Solving diffusion-like PDE for f(r,t)

I am trying to solve a partial differential equation like the following: where Sigma is mass density as a function of radial distance r and time t. I am expecting a diffusive behavior, and the ...
4
votes
0answers
62 views

How to put 2 or 3 NeumannValue conditions?

I want to solve numerically the heat exchange of a fin in transient state and two-dimentional, here is my attempt but instead of put DirichletCondition on ...
0
votes
0answers
41 views
1
vote
2answers
116 views

Back from transfer function (s-domain) to differential equation (in t-domain)

I've got the following transfer function (in the s-domain): $$\text{H}(s)=\frac{\text{C}s}{\text{RC}s+1}$$ Is there a function in Mathematica 10 that I can go back to the differential equation (in ...
4
votes
0answers
67 views

Avoid Evaluation of Function at NDSolve

I have a huge "black-box" f function, which I want to integrate. Let's define it: f[x_,y_,a_]:=a*Exp[-(a*10000)(x^3+y^3)] as ...
2
votes
2answers
110 views

Solving nonlinear 3rd order ODE over range from zero to infinity

Here are the code that I had tried but there is an error ...
2
votes
0answers
143 views

Bifurcation Diagram of Chua Circuit [closed]

I am currently working on a Bifurcation Diagram for Chua's Circuit but I am having trouble coming up with code for a bifurcation of a system of equations. The following equations are given in the ...
1
vote
1answer
252 views

Partial differential equation, Finite difference Method

For my research project I am trying to solve following partial differential equation in Mathematica (V[r]*ψ[u, v])/4 + Derivative[1, 1][ψ][u, v] == 0 with ...
-3
votes
1answer
91 views

Solving a first order PDE system [closed]

How can I solve using Mathematica the simple 1st order PDE system: $\frac{\partial P}{\partial x}=f(x,y,z)$ $\frac{\partial P}{\partial y}=g(x,y,z)$ $\frac{\partial P}{\partial z}=h(x,y,z)$ I want ...
5
votes
1answer
72 views

WorkingPrecision and NDSolve Method Plugin Framework

I'm studying some new numerical integration algorithms using NDSolve Method Framework to specify them. When I try to set ...
2
votes
0answers
78 views

Eliminating instabilities in a transient finite element solution at a discontinuity near t = 0

I have found a transient solution to the 1D heat equation where the initial condition is discontinuous. The results are accurate except for when time is small. The initial condition looks like this: ...