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

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2
votes
1answer
211 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
1
vote
1answer
387 views

Numerical solution of Schrödinger equation

I want to solve the following differential equation numerically. The geometry of the problem is as shown below. Electron 1 is located on the inner ring of radius $R_1$ and electron 2 is located on the ...
2
votes
1answer
92 views

About NDSolve with piecewise inputs

I am trying to solve numerically two differential equations with NDSolve. ...
3
votes
3answers
183 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
2
votes
1answer
54 views

Setting an upper limit in the NDSOLVE calculations

I have built a code to solve a system of differential equations in the form: $\displaystyle \frac{d(AB)}{dt}=kn(A)n(B)$ Here I present a small version of it: ...
0
votes
1answer
139 views

Error from NDSolve “Cannot find starting value for the variable”

I need help regarding this code. I have used NDSolve to find a solution. ...
3
votes
0answers
170 views

solve tricky nonlinear ODE on a grid

I've been working on the same question for a while now and would appreciate any advice on what I'm doing wrong or any direction on how to actually solve the problem. :) On xzczd's advice, I retried ...
1
vote
1answer
68 views

Adding algebraic functions to NDSolve

I want to define an integral function which depends on a system of ODE and is also used to NDSolve the ODEs. ...
3
votes
1answer
58 views

Setting a One Dimensional Function Equal to a Constant over a Specific Range

I am trying to take the output from NDSolve and create a variable equal to the solution except for a certain range of values. Here is the code I am trying to use ...
5
votes
0answers
83 views

Applying method of dominant balance directly to an equation

The non-linear equation $y''(x) = \sin k x y$ for $k\in \mathbb R$ cannot be solved analytically to yield a closed form solution. However, by applying the method of dominant balance one may obtain ...
6
votes
3answers
355 views

Using Grad, Div, etc in polar coordinates

I'm trying to use the newish functions Grad and Div to work with a PDE with circular or spherical symmetry and getting what looks to me like a wrong result. However, I'm not sure of this--perhaps I ...
2
votes
1answer
250 views

Getting errors NDSolve::nlnum, NDSolve::icfail)

I would like to plot the function v[r], and resolve this differential equation in spherical simmetry: ...
1
vote
1answer
93 views

How to plot vector field on a circle

I want to plot 1) vector field on a circle for the nonlinear equation and 2) theta dot and theta for different values of mu for the equation ...
2
votes
1answer
142 views

Dimensions problem with NDSolve

I'm having a difficulty to NDSolve a ODE due to the dimensions problem (according to the error message). Below is the code I have. First of all are functions: ...
4
votes
1answer
122 views

For loop to perform a shooting search in NDSolve

First comes the disclosure: I am very new to Mathematica and not so much a numerical guy in general. I am having a hard time using the for loop routine in Mathematica the correct way as well as ...
1
vote
1answer
71 views

From non-linear homogeneous DAE to linear state-space form

I have a non-linear homogeneous DAE $x' = F(y)$, $G(y) = 0$ where $x$, $y$ are vectors, $F$ is linear with constant coefficients, and $G$ is a polynomial with parametric coefficients. How can I ...
2
votes
1answer
70 views

Undetected WhenEvent with NDSolve

I was considering the following piece of code ...
0
votes
0answers
30 views

Fluctuations as initial conditions

I have two coupled partial differential equations in $u(x,y,t)$ and $v(x,y,t)$. I would like to set the initial conditions as fluctuations around some numbers, say, $4$ and $6$, for $u(x,y,0)$ and ...
2
votes
1answer
47 views

ndsolve interpolatingfunctions not shown/evaluated

Using this technique from Simon, I want to solve a matrix differential equation with a matrix that contains an explicit time-dependence(our variable), but I want to be able to solve this problem for a ...
1
vote
1answer
167 views

Periodic boundary condition

I want to solve a PDE as: $\frac{\partial u}{\partial t}=\frac{\partial u}{\partial x}$, with conditions: $u(x,0)=sin(\pi cos(x))$ and $u(x+2\pi,t)=u(x,t)$. I have solved it by hand and obtained: ...
0
votes
1answer
72 views

Can I tell DSolve to solve a first-order ODE by method of separation of variables?

I meet a first-order ODE $$\frac{dy}{dt}=\frac{a(\ln\frac{1-c}{1-y})^3}{\frac{b-y}{1-y}+\ln\frac{1-c}{1-y}},$$ where $a,b,c$ are constants. The ODE is subjected to the initial condition $y(t=0)=y_0$. ...
0
votes
0answers
81 views

How to solve boundary value problem with singularities at boundaries?

I have a boundary value problem, solving a system of differential equations with a singular boundary condtion (V[0] = 1/s, s->0) ...
5
votes
3answers
203 views

If statement within WhenEvent

I'm trying to integrate an equation with a periodic solution using NDsolve. I want to stop the integration after the derivative of my solution has become zero for ...
2
votes
1answer
107 views

Boundary condition not fully taken into account in DEigensystem?

Context Mathematica 10.3 now has the very nice DEigensystem function. ...
3
votes
2answers
396 views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
10
votes
3answers
514 views

Trying to find the asymptote to a function

I am trying to find the asymptote to a solution of a differential equation. I solved $x'(t) = \sin(x(t) + t)$ using NDSolve and plotted my solution. ...
1
vote
0answers
44 views

Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
1
vote
1answer
113 views

NDSolve : Second order ODE with variable coefficients

I have a second order ODE of the form : u''[x]+ p[x]u'[x]+ q[x] u[x]==0 ; with, ...
3
votes
4answers
202 views

Finding the “least” singular solution for NDSolve

I need to solve a ODE for a function $f_\sigma(x)$, where $\sigma$ is a free parameter to tune. All the solutions are supposed to be singular for some value of $x$, except one for a given value ...
3
votes
1answer
61 views

Need help understandig the output of `DSolve`

I give Mathematica (10) the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] And I have the following output: ...
1
vote
1answer
102 views

How can I handle interface thermal boundary conditions?

I am trying to solve a system of PDE´s coupled by interface boundary conditions, this is my code: ...
1
vote
2answers
89 views

Evaluation to true using DSolve - syntax errors?

Probably a stupid question, apologies, but I am getting an annoying error when I try to evaluate the following simple PDE $\frac{\partial C}{\partial t} = d \frac{\partial^2C}{\partial x^2}$ between ...
0
votes
0answers
60 views

FindFit giving many errors when given model produced by ParametricNDSolveValue

I am trying to use FindFit to determine 7 parameters using 7 differential equations based on data imported from Excel. A sample of the data is: ...
0
votes
0answers
32 views

StreamPlot, ListStreamPlot does not visualize vector field properly [duplicate]

I am reopening my question about empty stream plots. I couldn't find a choice for parameters that would give me a proper stream plot for the following example. ...
0
votes
2answers
105 views

How to display results of NDSolve

I am solving differential equation of second order ...
1
vote
2answers
159 views

StreamPlot, ListStreamPlot scaling issue [duplicate]

The following stream plot is empty and the x-axis exceeds $[-0.1,0.1]$ significantly. StreamPlot[{y, -100000 x - y}, {x, -0.1, 0.1}, {y, -100, 100}] Using ...
1
vote
0answers
55 views

Solving a 4th order PDE (Plate bending) [duplicate]

I'm trying to solve the following PDE but I'm getting this error. The PDE represents the bending of a thin plate. ...
2
votes
2answers
228 views

Attempting to use NDSolve to plot harmonic oscillator solutions

NDSolve[{ (-y''[r]/1880) + (470 (0.04077)^2 r^2 - 48 + 1/(1880 r^2)) y[r] == 0, y[0] = 0, y'[0] = 0}, y, {r, -4, 4}] I use this but get errors and am ...
1
vote
2answers
61 views

Plotting issue for nonlinear de

The following code with varying scaling parameter gives same plot. plz suggest correction. ...
2
votes
1answer
91 views

Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
0
votes
1answer
110 views

How to solve this DE?

The previous plot has executed. I have another code. This neither shows error nor shows any plot. ...
1
vote
2answers
112 views

Error NDSolve::nlnum1 from 2nd order ODE with 4 boundary conditions

I want to solve this 2nd order ODE with two initial conditions close to the origin (one to the function and the other to its derivative) and more two similar conditions for an endpoint. ...
7
votes
2answers
159 views

Unexpected warning from DSolve

I'm trying to solve this differential equation with respect to $x$ $$ \frac{d^2y}{dx^2}-\bigg(\frac{dy}{dx}\bigg)^2-\frac{1}{x}\frac{dy}{dx}=\frac{1}{x^2} $$ With boundary condition $y(1)=2, ...
0
votes
2answers
181 views

Solving non-linear differential equation

For my research project I need to solve the following integral ...
0
votes
1answer
106 views

FM NMOR in Cesium with Atomic Density Matrix package [closed]

I am trying to use the atomic density matrix package in Mathematica to simulate FM NMOR in Cesium. The example given in the package is for a specific system from J=1 to J'=0. I am trying to simulate ...
3
votes
1answer
93 views

How to determine the redundant equation in the set of DE?

my problem is messy, and I will use a simple problem to explain my problem. Suppose, we have a set of DE: ...
2
votes
1answer
85 views

Struggling with WhenEvent in NDSolve

I am doing some biological system modeling and trying to use WhenEvent in the initial conditions section of my NDSolve code to allow me to periodically change the value of a parameter (which I've ...
2
votes
1answer
160 views

NIntegrate::inumr: “The integrand `E^(-0.9τ1) DiracDelta[t-τ1] v[t-τ1] x[t-τ1]` has evaluated to non-numerical values ”

I am facing an interesting situation over here. The aim is to solve a system of IVP having an integral over a delay range. Here is my try ...
0
votes
0answers
53 views

ParametricPlot that worked in Mathematica 9 stops working in Mathematica 10

I've updated to Mathematica 10 and I am trying to plot the solution of a system of ODEs and I'm using exactly the same file that used to work in Mathematica 9, but now when I want to plot the solution ...
0
votes
0answers
67 views

Second Order ODE (Bessel Function) with a dependent variable in the BC

I have obtained an analytic solution to the following problem however I lack the knowledge to generate a numerical solution using mathematica. I'm reaching out to get an idea of what functions I may ...