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

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7
votes
0answers
336 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
7
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|) ...
6
votes
0answers
97 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
122 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] ...
6
votes
0answers
384 views

Numerically solve 2nd order differential equation with singularity

Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example: $$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$ where ...
5
votes
0answers
194 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
84 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
337 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 ...
5
votes
0answers
220 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 ...
5
votes
0answers
681 views

Controlling the time step in NDSolve?

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out ...
4
votes
0answers
66 views

Why do NDSolve and OutputResponse not evaluate non-analytic functions numerically?

test = OutputResponse[TransferFunctionModel[1/(1 + s), s], Exp[-(1/t)], {t, 0, 10}] does not evaluate. If Exp[-(1/t)] is ...
4
votes
0answers
154 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
193 views

Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem)

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
4
votes
0answers
272 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
707 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
106 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
87 views

1/0 encountered when solving an ODE

What can cause this error to show up? Clear[lambda, a, b, x, y]; ode = lambda y[x] + a b y'[x] + a (-1 + b x) y''[x] + y''''[x] == 0; DSolve[ode, y[x], x] ...
3
votes
0answers
52 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
166 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
228 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
3
votes
0answers
507 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
384 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,\\ ...
3
votes
0answers
355 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
39 views

DSolve breaks when the ordering of independent variables aren't proper?

I encountered this when trying to solve this problem with DSolve: ...
2
votes
0answers
39 views

Apply IC and BCs on Second - Order Linear PDE

I am now trying to solve second - order linear partial differential equation in that interested eq. has been separated into variables to simplify the procedure for Mathematica. Here is my equation; ...
2
votes
0answers
63 views

How to specify initial condition including integral equations in the case of the dirac equations?

Hi I am trying to solve a system of differential equation with NDSolve. The problem is I have like $3$ (maybe $5$) boundary conditions, but only $2$ differential ...
2
votes
0answers
92 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
2
votes
0answers
62 views

Locate Blow-up in NDSolve with Whenevent

At some point I get this error: ...
2
votes
0answers
71 views

Are there some other ways to solve a second PDE except DSolve?

I have a partial differential equation as follows: $$\frac{\partial p(x,t)}{\partial t}=\text{Dp} \frac{\partial ^2p(x,t)}{\partial x^2}-\frac{p(x,t)-\text{p0}}{\tau }$$ What I try to do was to get ...
2
votes
0answers
77 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
2
votes
0answers
54 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 ...
2
votes
0answers
85 views

How to solve system of differential equations of arbitrary order (symbolic tensors)?

I am interested in solving systems of ODEs symbolicly, keeping things with arbitrary dimensions for clarity. For example, assume that $x, f(x) \in R^N$ and $A \in R^{N \times N}$, how do I solve ...
2
votes
0answers
326 views

Solving a diffusion equation

I need to solve a particular diffusion equation with NO boundaries http://astronomy.nju.edu.cn/~chenpf/c/courses/fluid/pringle81.pdf equation (2.10) with nu = cost. ...
2
votes
0answers
169 views

NDSolve Issue with initial conditions

I am trying to implement a Poincare section for a gravitational movement on the plane $(x,y)$. Here is the code I wrote ...
2
votes
0answers
153 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
2
votes
0answers
238 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
0answers
246 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
0answers
523 views

ParametricNDSolveValue or NDSolve + fitting

I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
2
votes
0answers
461 views

Inconsistent boundary and initial conditions: BC ignored altogether

Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary: ...
2
votes
0answers
176 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
1
vote
0answers
13 views

How to fit data with numerical solution of system of parametric ODE?

I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function ...
1
vote
0answers
44 views

solution of differential equation with complex roots

How to find the solution of differential equation with complex roots For example of [{y^2 n[t]+ 2 k y n'[t] + n''[t]= M p sin(o t), n[0]==0, n'[0]==0}, n,t] given k lies between 0 to 1 which makes the ...
1
vote
0answers
52 views

Speeding up NDSolve for system of differential equations

I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ...
1
vote
0answers
30 views

Compiled NormFunction

I would like to use a user-defined NormFunction with NDSolve, e.g., NormFunction -> (Norm[Take[#, 2], \[Infinity]] &) which says that the infinity norm ...
1
vote
0answers
108 views

How to find a particular solution using NDSolve

I'm looking for a way to find a specific solution to a differential equation. As a simplified version of my problem, here's a similar setup for a simple harmonic oscillator problem. ...
1
vote
0answers
69 views

Solving two-component two-dimensional differential Equation with NDSolve (Brusselator Model)

I'm trying to solve a two-component two-dimensional reaction-diffusion differential equation system with Mathematica. The background of the model is the so called "Brusselator Model" where one can ...
1
vote
0answers
38 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
1
vote
0answers
59 views

Stiffness or Singularity

So trying to run some simulations based on a model I found in literature. I am by no means a Mathematica expert, or a mathematician for that matter. Initial I was getting a ...
1
vote
0answers
113 views

Runge-Kutta-2 on System

After spending some time using the Mathematica documentation and this Mathematica.SE answer, I implemented the Runge-Kutta-2 routines. I am hoping someone can validate what I did and tell me that it ...
1
vote
0answers
92 views

BVP system of nonlinear coupled ODEs

Here I am, trying to solve this system of coupled ODEs (up to a minus sign): $ u''=6u^5-(8+4a)u^3+(2+4a)u+\frac{2u((w^2-s)^2+bw)}{(u^2+c)^2}$ $ w''=\frac{4w^3-4bw+b}{u^2+c}$ with the boundary ...