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

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11
votes
0answers
185 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] ...
8
votes
0answers
2k views

Integro-differential equation

I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation, $$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
7
votes
0answers
217 views

Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
6
votes
0answers
104 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 ...
5
votes
0answers
73 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
votes
0answers
81 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
41 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
votes
0answers
115 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 ...
5
votes
0answers
164 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
211 views

Second order differential equation with boundary conditions solving repeatedly

I want to solve a second order differential equation in the interval[-1:1], which does not have a analytic solution, \begin{eqnarray} y''(x) &=& k \phi^2(x)y(x) \\ \phi(x) &=& ...
5
votes
0answers
362 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
94 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
423 views

Modeling neural excitation with a non-linear differential equation

I think I have a special problem and I am not sure how to search for an answer, so I thought I would try here. I am working with the so called FitzHugh-Nagumo model which describes very simple ...
4
votes
0answers
69 views

How do I programatically set up an NDSolve with lots of equations?

I'd like to set up... NDSolve[x1'[t]==2,x1[0]==0, x2'[t]==2,x2[0]==0, x3'[t]==2,x3[0]==0, x4'[t]==2,x4[0]==0, x5'[t]==2,x5[0]==0, ... etc Can I somehow use ...
4
votes
0answers
40 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
80 views
4
votes
0answers
69 views

Extraneous reaped data with NDSolve and WhenEvent

Bug introduced in 9.0 or earlier and fixed in 10.1 In exploring What is the range of values $x$ for which $f(x)$ is higher than $k$ over a given domain?, I came across the following strange ...
4
votes
0answers
347 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 ...
4
votes
0answers
406 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
4
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 ...
4
votes
0answers
525 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
120 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 ...
4
votes
0answers
256 views

Second-Order Feedback Pathways

I'm relatively new to Mathematica and I've tried searching and reading through the Mathematica documentation but I'm not able to find a good place to start. I want to model a simple, second-order ...
3
votes
0answers
66 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
87 views

Unknown (internal?) function with `DSolve`

I am solving With Mathematica 10 the following ODE system: DSolve[{B'[x] == -f[x]*Cos[l]*G[x], G'[x] == +f[x]*Sin[l]*B[x]}, {B,G}, x] The solution is almost ...
3
votes
0answers
87 views

Differential Geometry on a MeshRegion

For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke there somewhere) use it to calculate coordinate ...
3
votes
0answers
169 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
126 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
68 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
183 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
97 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
331 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
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
452 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
90 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
2
votes
0answers
59 views

How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence ...
2
votes
0answers
81 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
2
votes
0answers
50 views

ParametricNDSolveValue has a problem with complex numbers

Edited: I have simplified the example compared to before and narrowed the problem down a bit. I would like to use ParametricNDSolveValue as function for data ...
2
votes
0answers
146 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 ...
2
votes
0answers
94 views

Creating a nonlinear phase portrait

I am putting all of my code in one block for easy copy and paste. ...
2
votes
0answers
41 views

Axes in a vector plot

Consider: ...
2
votes
0answers
51 views

Update NumericalFunction in NDSolve

I have NDSolve` StateData from an NDSolve` ...
2
votes
0answers
65 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
2
votes
0answers
100 views

System of Partial differential equations

I am trying to solve numerically a system of 3 partial differential equations and I am facing a problem. My functions are f[x,t], ...
2
votes
0answers
68 views

DSolve solution of two unknowns

I have one problem with the solution of the system of two differential equations. I waited hours, but Mathematica didn't give me a solution. Is there any way to obtain the results if we suppose that ...
2
votes
0answers
98 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
2
votes
0answers
136 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, ...
2
votes
0answers
327 views

NDSolve and strange “nonlinear coefficients problem”

I'm stuck solving the following problem. I defined two functions as follows: $$ \varphi(\lambda) = \frac{\left((\lambda-2)^2-1 \right)^2}{4}$$ $$ \gamma(\lambda) = \varepsilon^2 ...
2
votes
0answers
104 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that MMA 10 has used Hermite method. I cannot find anything about this in MMA documentation. Is there nothing about Hermite method ...
2
votes
0answers
59 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...