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

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12
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0answers
200 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
7
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0answers
336 views

Problems when solving a nonlinear PDE system with NDSolve

The nonlinear PDE system is actually extracted from a research paper published in 2000 Here is the paper link The authors solved the system by using an ordinary differential equation integrator in ...
7
votes
0answers
515 views

Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
6
votes
0answers
47 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
6
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0answers
124 views

Heat convection differential equations from 1952 - Mathematica “fails to converge”

I am trying to solve a fundamental problem in analytical convective heat transfer: laminar free convection flow and heat transfer from a flat plate parallel to the direction of the generating body ...
6
votes
0answers
431 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
5
votes
0answers
64 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 ) ...
5
votes
0answers
72 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 ...
5
votes
0answers
148 views

DSolve returns an answer that is not a solution

Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve. The following DSolve command returns an answer to the ...
5
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0answers
101 views

Compiling FoldList implementation for RK4

Original I'm looking to write an integrator for a function of two variables. Here is my implementation for the RK4 update rule using FoldList. ...
5
votes
0answers
56 views

Why DSolve doesn't handle duplicate boundary condition

This code works well. DSolve[{y''[x] + 10 y'[x] == 0, y[0] == 0}, y[x], x] (*{{y[x] -> 1/10 E^(-10 x) (-1 + E^(10 x)) C[1]}}*) But why mma gives ...
5
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0answers
230 views

Alternatives to FiniteElement as Spatial Discretization Method for NDSolve

Finite Element Programming: [...] It is possible to skip this section and continue with the discretization stage and make use of the initialized data structures ...
5
votes
0answers
1k views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
5
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0answers
100 views

Modify NDSolve`StateData (if possible)

I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData. Now, the problem is, I'm not used to ...
5
votes
0answers
603 views

Kalman filter by hand

I am now learning the Kalman filter and wants to implement it by hand to understand it better. To be specific I want to first simulate a sequence of data by $$ \dot x=Ax+Bw\\ y=Cx+Dv,\\ ...
4
votes
0answers
46 views

Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain

I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ...
4
votes
0answers
109 views

new kernel crashes using DSolve in 10.3.1

Update: I added small movie showing the crash, since others who tried it so far could not reproduce it on their system. Original question I am finding new problems with ...
4
votes
0answers
78 views

unhandled win32 exception in WolframKernel.exe in DSolve of non-linear ODE in one variable

Installed 10.3.1 and started to run some old ode's. in V 9, this ode used to return unsolved, which is ok, but in 10.3.1 now the kernel crashes. This is on windows 7, 64 bits. I wonder if this also ...
4
votes
0answers
45 views

Strange behaviour of suggestion bar to solve an ODE, potential bug

InputE^(-(1/2) x[t]^2) (Derivative[1][x][t]^2 - (x^\[Prime]\[Prime])[t]) == 0and evaluate, then press the solve ode button on the suggestion bar. It will return ...
4
votes
0answers
122 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
0answers
36 views

Weird behaviour for a vector InterpolatingFunction inside an NDSolve

I have run into some weird behaviour on the part of NDSolve which I find pretty bizarre and which I would like to understand better. Suppose, for the sake of ...
3
votes
0answers
85 views

Constructing the coefficient matrix in discretization of a PDE

In order to solve the following two dimensional PDE $$\frac{\partial u(x,y,t)}{\partial t}-\frac{1}{2} \sigma _1^2 x^2 \frac{\partial ^2u(x,y,t)}{\partial x\, \partial x}-\frac{1}{2} \sigma _2^2 y^2 ...
3
votes
0answers
96 views

How to solve partial differential equation

How to solve in Mathematica this partial differential equation: $0.5\frac{\partial t(x,y)}{\partial x}+1.5\frac{\partial t(x,y)}{\partial y}+t(x,y)=y\cdot \sqrt{1+x^{3}}$ with condition $t(1,y)=y+2$? ...
3
votes
0answers
41 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 ...
3
votes
0answers
54 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 ...
3
votes
0answers
109 views

Complex boundary conditions and NDEigensystem

I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem. The Navier equation is given by $\nabla^2 \vec u + (p^2 - 1) ...
3
votes
0answers
155 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 ...
3
votes
0answers
47 views

Does NDSolve automatically simplify the system of equations for Hermitian matices?

I am currently starting to solve numerically a system of differential equations like this: $\dot{A}(t)=S(A)A(t)$ Here, the matrices are of dimension $d\times d$. $S(A)$ is some superoperator that ...
3
votes
0answers
66 views

Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
3
votes
0answers
90 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let ...
3
votes
0answers
73 views

Verification of results given by NDSolve

I am trying to solve a system of ODEs using NDSolve. The differential equations used are obtained by applying method of lines to actual governing equation. The system includes differential equations ...
3
votes
0answers
246 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
3
votes
0answers
77 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 ...
3
votes
0answers
145 views

How to control pedestrians to enter the simulation region with random functions?

I am working on simulating crowds of a cross-typed region, given that pedestrians entering from 4 gates of north, east, west and south, ...
3
votes
0answers
205 views

Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
3
votes
0answers
179 views

Increasing MaxPoints in NDSolve results in memory issue

I am interested in increasing "MaxPoints" in NDSolve's "MethodOfLines" in attempt to increase the resolution of the plot of the solution of linearly damped wave equation with transparent boundary ...
3
votes
0answers
595 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
3
votes
0answers
70 views

Error solving third order ODE in version 10. No error in V9. DSolve`DSolveKovacicDump`

This is an ode which is solved with no error in V9, but gives a very strange error in V10. Is this a regression bug? On version 9, the ode is solved with no error ...
3
votes
0answers
244 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = ...
3
votes
0answers
124 views

Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected ...
3
votes
0answers
413 views

Numerically solving a system of PDEs where one function is composed with the other

I'm trying to solve the following system using NDSolve: $$ \begin{align} u_t(x,t) &= u_{xx}(x,t) - v(x,t) \\ v_t(x,t) &= u(v(x,t),t) \end{align} $$ with ...
3
votes
0answers
841 views

Solving a diffusion equation

I need to solve a particular diffusion equation with NO boundaries (see eqn. (2.10) in: Ann. Rev. Astron. Astrophys. 19:137-62 (1981).) with nu = cost. ...
3
votes
0answers
1k views

Using NDSolve for Integro-Differential Equations

I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are: ...
3
votes
0answers
472 views

Numerically solving PDE with high precision

I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...
2
votes
0answers
23 views

WhenEvent and Resetting of Variable in PDE when operation succeeds

I have had success in using WhenEvent to reset or change a variable within NDSolve with ordinary differential equations. My ...
2
votes
0answers
84 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 ...
2
votes
0answers
109 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 ...
2
votes
0answers
100 views

Bifurcation Diagram of Chua Circuit

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 ...
2
votes
0answers
71 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: ...
2
votes
0answers
55 views

WhenEvent behavior changed from v9 to v10 - how to fix the code?

A couple of years ago I asked a question about solving n-body systems with NDSolve and detecting collisions with WhenEvent. I ...