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

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2
votes
1answer
988 views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
1
vote
1answer
232 views

Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
0
votes
0answers
370 views

Solving differential equations with sums (power series)

I have sets of 10 differential equations, but for this purpose I'll demonstrate what I need on one example that can be solved by hand. My equation is this: ...
8
votes
3answers
676 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
0
votes
0answers
696 views

PDE problem with initial and boundary conditions

I'm new to mathematica and I don't know what I do wrong, I have written the following PDE problem, with both initial and boundary (four in total) ...
12
votes
1answer
894 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
1
vote
1answer
266 views

Solve a total derivative - independent vs. dependent variables

I am trying to force mathematica to solve a generally defined function for d lp: In a reduced version, w depends on l2, ...
0
votes
2answers
1k views

Solving a system of nonlinear coupled ODEs

I tried using NDSolve to solve the following system of equations: ...
1
vote
0answers
152 views

NDSolve error when solving pde

I am trying to calculate speed of viscous fluid in a rotating hollow sphere. The sphere is rotating round z axis. The fluid is incompressible. I used Navier-Stockes equations. The only boundry ...
1
vote
0answers
179 views

Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
0
votes
0answers
104 views

Nested NDSolves with functions

I am trying to solve a system of nested differential equations, and have attached my code below. The first section is some variable declarations, then I solve my first diffeq and store the solution to ...
0
votes
1answer
69 views

LMS distance from a point to an InterpolatingFunction

I have a short script to NDSolve a second-order nonlinear BVP, which as its output produces an InterpolatingFunction object. I ...
6
votes
1answer
457 views

Getting clearer StreamPlot output

When I do a StreamPlotof a rather complicated pair of differential equations, it loses some details. For example: ...
11
votes
1answer
669 views

Solving Killing equations

Is it possible to solve Killing equations in Mathematica for a general vector? I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this. ...
3
votes
3answers
448 views

StreamPlot using NDSolve gives error messages

StreamPlot[{x[0], x'[0]} /. NDSolve[{x''[t] == 1, x'[0] == v0, x[0] == x0}, {x, x'}, {t, 0, 1}], {x0, -2, 2}, {v0, -2, 2}] The above code gives me the errors ...
0
votes
1answer
151 views

Checking differential equation solution

I have this differential equation: eq=D[ψ[r],r]+A*ψ[r]-(B/(A*r))ψ[r]==0; And DSolve sucessfully solves it: ...
2
votes
1answer
339 views

Avoiding zero (empty set) solution with NDSolve

I'm trying to use NDSolve for a chemical kinetics equation where the rate of conversion is given by this relationship as typed in Mathematica: ...
2
votes
0answers
461 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. ...
5
votes
0answers
273 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 ...
4
votes
3answers
346 views

Plotting the direction field of a differential equation

I have to sketch the direction field for the following differential equation: $$\frac{dy}{dx}=\frac{-0.02 y +0.00002 xy}{0.08 x-0.001xy}$$ This is the code I used, which gives an incorrect plot: ...
1
vote
2answers
126 views

NDSolve error---equations expected [closed]

I keep getting an error trying to used NDSolve for three coupled equations. It works in another programming language, but I am having trouble apparently writing it ...
2
votes
0answers
236 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
1answer
607 views

Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
3
votes
2answers
535 views

FindFit for a differential equation model with multiple variables?

I'm trying to figure out how to use FindFit with a multivariable differential equation model and data. I've successfully made it work for the one-variable version ...
2
votes
1answer
177 views

NDSolve much slower when using InterpolatingFunctions inside

I am solving an ODE system with Mathematica. Let's say the system is of the form (to simplify). ...
3
votes
2answers
199 views

DSolve vs a system of differential equations

I'm trying to solve a simple system of differential equations. ...
0
votes
0answers
125 views

Solve differential equation with undetermined constants making the assumption that the constants are positive

I want to solve: eqn = D[f[w], {w,2}] + (3/2 c^2 k Exp[c w] - 9/4 c^2 k^2 Exp[2 c w]) f[w] + m^2 f[w] sol = DSolve[eqn == 0, f[w], w] with the assumption ...
0
votes
0answers
224 views

Defining extra boundary conditions for NDSolve?

I have a second order reaction / diffusion type ODE of the form $\frac{D_{o}}{r^2} \frac{d}{dr}\left(r^2 \frac{dC}{dr} \right) - \frac{aC}{C+k} = 0$ where $a, k$ and $D_{o}$ are constants and $C$ is ...
-1
votes
1answer
184 views

Linking two differential equations

The solution and plot of the Differential equation is $\frac{d^2S(r)}{dr^2}+\frac{1}{r}\frac{dS(r)}{dr}-S(r)+3S^3(r)=0$ ...
-1
votes
1answer
455 views

plotting the solutions of system of differential equations [duplicate]

The following code include the system of differential equations: ...
1
vote
1answer
192 views

Dsolve too slow — is there anyway around?

I am trying to solve: ...
3
votes
1answer
262 views

Modelling the effect of a structure on a “tsunami” (hyperbolic wave equation)

So, the hyperbolic wave equation can be quite easily solved in Mathematica like this: ...
2
votes
2answers
201 views

How to pick out specific parts of the solution of a differential equation efficiently?

I'm trying to solve a set of differential equations (in parallel) and then select specific parts of the solution. What I have at the moment (see below-I've simplified the differential equations, in ...
2
votes
1answer
72 views

Incorrect information displayed when slider is moved (intermittent)

All, the following code graphs 10 different solutions for a first order ODE and allows the user to modify certain equation parameters to see how the graph is affected: ...
4
votes
2answers
539 views

DSOLVE for tenth order boundary value problem

I am currently using Mathematica 9 to find solutions for higher order ordinary differential equations. The following was my input for a tenth order boundary value problem (BVP): ...
2
votes
2answers
541 views

How to generate 2D FEM mesh in Mathematica?

To generate 3D mesh TetGen can be easily used. Are there similar functions (or a way to use TetGen) to generate 2d mesh? I know that such functionality can be easily implemented but I would like to ...
7
votes
2answers
434 views

Only final result from NDSolve

Finally I started to play with differential equations in Mathematica. And I have faced the problem, which seems too me so basic that I'm afraid this question is going to be closed soon. However, ...
0
votes
0answers
333 views

Plot basins of attraction using separatrices for particular pendulum

How can I plot the stable and unstable separatrices to make a graphic of the basins of attraction of this differential equation? ...
2
votes
1answer
322 views

Use output of NDSolve as an integration limit of NIntegrate

I've been working on a ODE, for a function y[t], that, due to it's complexity, has to be solved numerically. I then need to use the results of NDSolve, which I ...
3
votes
1answer
300 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 ...
6
votes
1answer
537 views

Modelling a Rocket Launch using NDSolve

I'm trying to model a rocket launch with Mathematica but I've run into a little problem since I don't know how to turn the thrust off. I'm using Newton's Law of Universal Gravitation plus an added ...
4
votes
1answer
234 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
0
votes
1answer
549 views

Bifurcation diagrams for system of equations

I am interested in constructing a bifurcation diagram for parameter a in the dynamical system given in the code below. I want to see how parameter changes affect the stability of the system. The ...
0
votes
1answer
449 views

Can graph interpolating function, but not use it. Any thoughts?

When solving a system of differential equations numerically, I get two interpolating functions. I can graph both of these, but when I try to evaluate either of the functions at a point, it just spits ...
0
votes
2answers
195 views

Interpolating a ParametricFunction

Original domain of my independent variable t is 0 to 10 nanometers, but in Mathematica (as in most numerical software), it's good idea to solve differential ...
0
votes
0answers
285 views

NDSolve for a large system of coupled (complex valued) ODEs

The system under consideration here is a generalization of the one I discussed in this problem. Qualitatively, I am trying to solve a system of coupled nonlinear (up to order 4 in the dep variables) ...
4
votes
1answer
271 views

Changing a wave simulation

I want to adjust some code that I found on this Wolfram Demonstration: http://demonstrations.wolfram.com/WaterRipplesPassingThroughASlit/ Basically it shows a wave passing through a single slit. I ...
3
votes
2answers
402 views

Ploting a 3D vector field using Manipulate, VectorPlot3D and NDSolve

My aim is to plot a vector field of the following system with a few trajectories: $$r'(t)=i-l.r(t)-\text{ux}. r(t). x(t)-\text{uy}. r(t). y(t) \\ x'(t)=\text{ex}. \text{ux}. r(t). x(t)-\text{mx}. ...
4
votes
0answers
335 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 ...
1
vote
1answer
819 views

3D Phase Portrait with direction fields and sample solution curves [duplicate]

I have seen NDSolve and ParamtericPlot3D used for things like the Lorenz Attractor, but was wondering if there is a way to draw a 3D phase portrait for a system. Something akin to this: ...