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

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3
votes
2answers
418 views

Using periodic boundary conditions in NDSolve

I need to solve a 2D linear elliptical equation in polar coordinates using NDSolve, but I can’t seem to get Mathematica to accept the required periodic boundary conditions. My actual differential ...
10
votes
2answers
295 views

How to use NDSolve with discontinuities at internal boundaries?

I don’t know how to impose discontinuous internal boundary conditions (BCs) in NDSolve, so I’ve set up an example problem to illustrate my issue. Consider the simple first-order ODE for $f(z)$ on the ...
14
votes
2answers
599 views

Solve differential equation using a integral form boundary condition

I have a second order differential equation and I want to solve it analytically (DSolve) and numerically (NDSolve) with ...
2
votes
2answers
130 views

How can I check that the general solution obeys the original differential equation?

For example: I solved the following differential equation: y''[x] == (λ x^(3/4) y[x])/Sqrt[1-x] that 0<x<1 with the ...
1
vote
1answer
175 views

How can I use NDSolve with a variable parameter?

I'm a new user and I can't understand how to solve this function for variable values of vr (for example vr from 0 to 5 in steps ...
0
votes
1answer
71 views

Solving differential equation (Analytical or Numerical)

I want to solve the following differential equation for $0 < x < 1$ ...
0
votes
1answer
71 views

NDSolve Problems with Cardiovascular Modeling [duplicate]

I am trying to use 27 simultaneous differential equations to model the cardiovascular system. I have the following code, however, the output isn't giving interpolating functions, but rather another ...
3
votes
3answers
170 views

When using NDsolve, how to determine the positions of steady states?

I am currently trying to numerically solve a set of ordinary differential equations of chemical kinetics. However, I want to implement perturbations only when system reach steady states. For example ...
1
vote
1answer
160 views

Animating a 3D shape along path a (2D and 3D) parametric function curve [Update]

I have a 3D object under the action of gravity field.The trajectory of path is a parabola.I would like to animate , as in the example GIF. ...
6
votes
1answer
230 views

Confirming conservation laws for complex valued functions

Consider the nonlinear Schrödinger equation (I would like to do this for a more complicated set of equations, but to gain understanding I'll consider this simplified case) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
-2
votes
1answer
46 views

NIntegrate a function containing NDSolve

I am having an issue integrating a function for which I am getting values for when I evaluate it. ...
4
votes
2answers
370 views

DSolve misses a solution of a differential equation

[Note that in the cited duplicate, DSolve not finding solution I expected, the general solution returned by DSolve is missing a solution for quite different reasons ...
1
vote
1answer
96 views

How do I solve this ODE numerically in Mathematica?

I want to solve these equations numerically in Mathematica and plot them. \begin{equation} u'(t)=1.5\,u(t)\,v(t)-u(t) \space \space \space \text{and} \space \space u(0)=0.001 \end{equation} ...
1
vote
1answer
81 views

Solving differential equation but keeping showing running

I am trying to solve this differential equation, see the command below. But the cell keeps showing that it is running without giving any answer for a very long time. Eventually I had to abort it. Does ...
0
votes
1answer
141 views

KdV equation - wavebreaking and Galerkin method

I want to show how a wave given by the initial condition: $$ \begin{equation*} \begin{split} u(x, 0) = \left\{\def\arraystretch{1.2}% \begin{array}{@{}c@{\quad}l@{}} 1 - x^2 & \text{for ...
3
votes
3answers
166 views

NDSolve and Plotting

So I am having an issue using NDSolve and plotting the function. So I have two different NDSolve calls in my plotting function. ...
4
votes
1answer
120 views

Substituting ParametricNDSolve for NDSolve

This is my first post so let me know if I need to format things differently. I have been using NDSolve for most problems which optimize parameters for ODEs. I believe that ParametricNDSolve would be ...
0
votes
0answers
63 views

Finding when a ODE returns to starting position

I am trying to discover when these ODE return to their start position. I am using coordinates that have a periodicity of {Pi/2, 2Pi, 2Pi}. To accomplish this I have had to use mod. The ODE are ...
0
votes
0answers
132 views

How to optimize a cost function which involve the solution of a ODE system using the NMinmize?

I have created a cost function, the value of which depends on the solution of a ODE (ordinary differential equation). The parameters of the ODE are not determined, and my goal is to determine them ...
0
votes
1answer
141 views

How to find the zero of a function defined by a non linear differential equation

I need to find the zero of a mysterious function sigma defined by a differential equation of the following form $$u*\sigma'(u)+(1-\chi_0)*\sigma(u)+\sum_{k=1}^{D} ...
3
votes
1answer
74 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
2
votes
2answers
110 views

Finding Minimium Periapse Distance Between Spacecraft and Planet

I have the following simple model that simulates a spacecraft orbiting Mars. What I'm hoping to do is be able to find the periapse radius of the spacecraft as I did below, except instead of using ...
5
votes
0answers
67 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
1answer
342 views

Why does DSolve give a different result than NDSolve?

When I try DSolve to solve a system: ...
2
votes
0answers
149 views

How to use WhenEvent with several conditions?

I would like to use StopIntegration in WhenEvent, when more than one condition should be checked. For example, in the code below ...
1
vote
1answer
437 views

Numerical solutions of Gross-Pitaevskii equation [closed]

I am trying to solve the Gross-Pitaevskii equation numerically and using NDSolve, but this seems to be a dead end. The problem is boundary and initial conditions ...
6
votes
1answer
249 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
0
votes
1answer
90 views

Why empty plot (Dsolve solution)?

When I try to plot the DSolve output, I get empty plot. Here is the code ...
2
votes
1answer
163 views

Gradients of the NDSolve PDE solution

I would like to understand, how to obtain gradients of the PDE solution obtained with NDSolve. To be precise let us consider a Laplace equation from one of the examples: ...
0
votes
0answers
149 views

NDSolve polar coordinates

I need to define a function namely "u" as u[r,Theta,t] in polar coordinates. In fact I need to solve the below equation preferably analytical while numerical solution is also desirable where Alpha ...
4
votes
1answer
265 views

How to vary finite difference approximation order in `NDSolve` at boundaries

According to here, NDSolve, when using the method of lines, creates partial derivatives in the spacial coordinate (lets talk just about one spacial coordinate for ...
0
votes
0answers
70 views

Isolate graphic components in Manipulate

I have cobbled together two Wolfram Demonstration files to produce the code below. My objective is to generate the phase plane plot on the left side of the output by clicking in one of the regions of ...
2
votes
2answers
261 views

Solving coupled first-order autonomous differential equations

I am trying to run a simulation of a circuit to observe chaotic behavior, and have obtained a set of differential equations from an analysis of the circuit. I thought perhaps I could produce a plot ...
1
vote
0answers
111 views

How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
5
votes
2answers
345 views

DSolve returns a “wrong” solution

This wrong solution exists from mma9 to mma10.1: ...
9
votes
1answer
160 views

Kernel Crash while using “ValuesOnGrid” method of InterpolatingFunction

Bug introduced in 10.0.0 and fixed in 10.2.0 I was experiencing some kernel crash while using "ValuesOnGrid" method of an ...
0
votes
1answer
74 views

Substituting inside a differential equation

x y''[x]+2y'[x]+l^2 x y[x]==0/.y[x]->Cos[x] I think above code shows what I want to do quite clearly. How do I make it happen. Only y[x] is replaced.
0
votes
1answer
162 views

Which platform is ideal for performance?

I have been using NDSolve, and I noticed that when you decrease the MaxStepSize, possible singularities are resolved. If I ...
0
votes
1answer
113 views

DSolve with piecewise coefficeints wrong, why?

sorry if this is a duplicate (I am pretty sure) but I was not able to find the question. I am playing around with DSolve with variable coefficients. In the documentation it is said, that DSolve can ...
2
votes
1answer
318 views

Piecewise Function within NDSolve

So I am quite new to Mathematica and programming in general and I am running into an issue while trying to use the numerical diff eq solver (NDSolve) within mathematica. This is what my code looks ...
2
votes
2answers
235 views

Strange Boundary NDSolve Problem

Mma10.1 doesn't work with the following boundary problem: ...
1
vote
1answer
55 views

Multiplying two parametric solutions

I'm solving two (1-parameter) differential equations and I want to plot the product of their solutions, how do I do this? Here's the code, ...
0
votes
2answers
119 views

Formatting the results from solving a differential equation

{{x[t] -> 600 (t + I π t - 50 Log[50] + t Log[50] + 50 Log[50 - t] - t Log[-50 + t])}} After solving a differential equation, I get an answer in a form where I ...
8
votes
2answers
535 views

How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
2
votes
1answer
199 views

NDSolve doesn't work for this simple differential equations

I try to use NDSolve to do this partial differential equations, but the result is wrong... The source term is a Gaussian pulse as time and an exponential decay with the depth z. The result should be ...
5
votes
1answer
137 views

Unknown (internal?) function with `DSolve`

Bug introduced in 8.0 or earlier and fixed in 10.3.0 I am solving With Mathematica 10 the following ODE system: ...
0
votes
1answer
80 views

Solving differential equation with Variable constans?

How do I solve the following differential equations using Mathematica under the assumptions: If Abs[r[t]]<50 ->A=0.5;B=2; AND ...
6
votes
1answer
326 views

3D FEM with holes

I'm trying to create a finite element mesh with some spherical holes. To my mind the behavior is erratic but generally fails. I'm using MMA 10.0.2. In the following 3 different sets of holes are ...
-4
votes
1answer
102 views

How do I solve and graph this coupled PDE?

How can I solve and graph v1 versus t and v2 versus t for a given x? Let A = 3, p = 2, B = 4. At t = 0, v1 = 2, v2 = 2. For the graph the range of t is [0,60].
1
vote
1answer
79 views

Assymptotically Solving ODE with free parameters

I have a first order ODE, $F(y[x], y'[x], A, B) = 0$. I want to solve this numerically (with the boundary value $y[1] = i$ ) but also with the following requirements: A and B are free parameters which ...