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

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Solving a complicated integro-differential equation

I'm trying to solve the integro-differential equation: $-(1+z) H(z) \frac{d f_{i}}{dz} = J_{i}(E',z) - f_{i} \sum_{j} n_{\nu_{j}} \sigma_{ij}(E',z) + \int_{E'}^{\infty}dE~\sum_{j,k}f_{k} n_{\nu_{j}} ...
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0answers
18 views

Simple heat equation with exponential reaction term [duplicate]

This is the heat equation that i want to solve $${\partial T\over\partial t}={{1\over r^2}{\partial\over \partial r}(r^2{\partial T\over \partial r})+qAC_0exp(-E_a/RT) } \ \ \ 0<t<10, \ \ \ 0<...
2
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2answers
124 views

How to plot an Eddington-Finkelstein diagram

I need to plot the same thing as what is shown on the third picture of the site below (sorry, I'm unable to poste that picture here) : http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/...
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1answer
45 views

PolarPlot with InterpolatingFunction not working?

So I have solved a PDE with NDSolve which returns h -> InterpolatingFunction. I can happily plot the results with ...
3
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1answer
162 views

How can I combine NDSolve[] with NSolve[]

Consider the two below ODEs with following dependent B.C. In the boundary conditions $k$ is an unknown. $$y_1''(x)=x$$ $$y_2''(y)=0$$ $$y_1(1)=y_2(1)$$ $$y_1(-k)=y_2(-k)$$ $$\frac{\text{dy}_1(1)}{\...
1
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0answers
200 views

Wave equation PDE with changing boundary condition [closed]

This is my first post here, normally with mathematica I will solve out the PDE using eigen function expansion or separation of variables and then model the solution in mathematica. However this time I ...
1
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2answers
85 views

Stop Integration in NDSolve

The following code executes properly for some choices of initial points and parameter c, but fails for other choices. Could the failure be due to computation outside of the defined t, x, and y ranges? ...
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0answers
269 views

Problem with NDSolve in Mathematica 9 / 10

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ...
6
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2answers
817 views

PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
7
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2answers
116 views

Bug in NDSolve/WhenEvent?

Bug introduced in v10. I'm fairly sure the following is a bug, and I would normally just report it to WRI. However, this is related to my answer to When using NDsolve, how to determine the ...
-2
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1answer
65 views

Neumann and Dirichlet eigenvalue problem - Eigenfunctions on the square [closed]

I don't know if I am in a good place to ask my question, but I'd like someone to create a visual support for a problem of mathematics. I was wondering what is the fundamental different between a ...
3
votes
3answers
212 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 ...
5
votes
3answers
1k views

How to deal with zero in NDSolve in mathematica?

I would like to solve the following ODEs $$\begin{cases} x'(t)&=y\\ y'(t)&=-y(t)/t-e^{x(t)},\\ x(0)&=1,\\y(0)&=0, \end{cases}$$ (EDIT : The second equation used to be $y'(t) = -x(t)/...
5
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3answers
148 views

NDSolve divide-by-zero trouble

So I have a set of differential equations (which I know are analytically integrable) but I want to integrate them numerically to get the form of the solution (the solution is not explicit and hence I ...
4
votes
2answers
897 views

Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
1
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2answers
344 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
0
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1answer
43 views

Speeding up WhenEvent + NDSolve (Performance tuning and handling instabilities)

I am solving a non-linear partial differential equation using NDSolve. The equation models a liquid film on an isothermal solid substrate. As a result of various fluid physics mechanisms such as ...
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0answers
28 views

Evaluating solution from NDSolve at a specific point

sol = NDSolve[{eq, iv}, {f[x, t]}, {x, 0, 1}, {t, 0, 10}]; sol[0,1] I want to evaluate the solution from NDSolve at any given point, but when I do the above, ...
0
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1answer
45 views

system of differential equations 3 DSolve [closed]

dS/dt = a - dS - λ S I + β R dI/dt = λ S I - (d + m)I dR/dt = m I- (d + β)R Solve the above equation and plot the curve.
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0answers
31 views

Difference between using NIntegrate and Integrate inside NDSolve?

The differential equation I am considering depends on an integral, which I would like to solve with NIntegrate (since it will gets more complicated and thus I have to use NIntegrate later). My code ...
0
votes
2answers
41 views

DSolve non linear DE

probably my problem i´m gonna ask seems ridiculous and quite basic. I want to solve an equation with the following code, where a,b,c are parameters. But surprisingly they don´t appear in the solution. ...
3
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0answers
57 views

Two questions about “wraparound” with “Event” method

I am learning EventLocator method from the document center. As for the following code (copy from this document) solving the sine-Gordon equation, it uses the ...
2
votes
1answer
379 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
1
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0answers
50 views

Any possible to save a 'partial' result of NDSolve when it was aborted due to insufficient memory?

I have run a NDSolve code for an extremely long time. Unfortunately, it was aborted because there was insufficient memory available to complete the computation. At ...
0
votes
1answer
116 views

Plotting Limit Cycle

I have Lotka Volterra Equations where the prey equation is modified. The Equations are x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t] y'[t]=-c*y[t]+d*x[t]*y[t] To plot the ...
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0answers
106 views

Fitting Three-Dimensional Data with Parameters

I have been trying to fit a model of rate equations to data of three dimensions. The rate equations in my model are as follows. ...
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0answers
57 views

Numerical fitting trajectory to model that has NDSolve

I have a model which describes the motion of an object on a plane. ...
0
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0answers
52 views

Double Integral with NDSolve!

I have fivefold multiple integral and I wanted a speed calculations.I came across on this Question and had already begun the problems. Here is a toy example with simple double integral: ...
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1answer
55 views
3
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1answer
56 views

Why does the Part::partw error appear when using DSolve?

I solved the following ordinary differential equation for $F(x)$ using DSolve in Mathematica $$ \begin{align} \begin{split} & A x^2 (x^2 + 1) F'''(x) - \left(3 A (b - 2) x^3 + a x^2 +A (b - 2)x +...
0
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1answer
61 views

Diffusional equation [closed]

I am still new to Mathematica. I'm trying to solve a diffusional equation ...
0
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1answer
56 views

Can I solve system of differential equation in a matrix form?

I'd like to solve simple system of differential equations: x'[t] == 6x[t] - 6y[t], y'[t] == x[t]-2y[t]; but I want to avoid formulas like DSolve[{x'[t] == 6x[t] - 4y[t], y'[t] == x[t]-2y[t]}, {x,y},...
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0answers
24 views

How many boundary conditions are required for two coupled Non-linear ODE in two variables?

I'm using NDSolve to solve the following two coupled Nonlinear ODEs in two variables: Equation1 = Equation2 = It can be seen that the level of nonlinearity is very high. I have solved the ...
0
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2answers
44 views

Produce several file outputs within one calculation

I have a differential equation which I solve with NDSolve. With the obtained solution I calculate some quantity. Then a constant in the ODE will be raised (until a ...
1
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0answers
38 views

Looking under the hood of DSolve

Is it possible to print out information about the algorithms DSolve uses to solve a differential equation? I'm looking for something similiar to this Maple procedure. It lets you specify how much ...
2
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1answer
78 views

Using loops to draw multiple polygons and discretizing them

I am trying to plot the first eigenvalue of the Laplacian operator with zero Dirichlet condition on following figure against decreasing values of $\varepsilon$. I used ...
4
votes
1answer
98 views

Issues with modeling pulses in a very simple system of DAEs

Bug introduced in 10.4.1 or earlier Bug has been confirmed by WRI [Case:3594387]: It does appear that the NDSolve function is not behaving properly in this case and an incident report has been ...
1
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1answer
49 views

Using NIntegrate inside NDSolve

I need to use NIntegrate inside NDSolve, for example: ...
4
votes
1answer
522 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by <...
0
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1answer
57 views

NDSolve error: Step Size is effectively zero; singularity or stiff system is suspected

my current project is numerically solve the Friedmann equation: (a-dot / a)^2 = H_0^2 (sigma_r / a^4 + sigma_m / a^3 + sigma_lambda + simga_k / a^2) What I did was split my equation into two ...
0
votes
1answer
51 views

Solving boundary-value problems within a specified region

Is it possible to use DSolve with non-initial boundary conditions? For example, eqn = a == b x'[z] + c x[z] over the region 0 to L, something like ...
3
votes
1answer
334 views

Problems with NDSolve and partial differential equations of several variables

Suppose we have the following partial differential equation: $$ 0 = \frac{ \partial w }{ \partial \tau } + \left( w + \sqrt{ h + \beta } \right) \frac{ \partial h }{ \partial \chi } $$ where $w$ = $w(\...
2
votes
1answer
322 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
2
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0answers
83 views

Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
0
votes
1answer
56 views

Writing PDE boundary conditions with derivatives, More general than Neumann

I am solving 2D Laplace equations on f[x,y] with boundary conditions SomeVector[x,y].Grad[f] == 0 This is more general than Neumann. Is there a way to set such boundary conditions for a curved ...
2
votes
1answer
167 views

solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...
0
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1answer
55 views
1
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1answer
102 views

Euler-Bernoulli cantilever beam with parabolic load

How do I obtain the displacement in the free end of a bar with Parabolic load (I.e. in point with length L)? I found the information on a site, but only I found for uniform load. Someone who ...