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

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1answer
64 views

Manipulating of non linear differentials equation

I want to manipulate non linear differential equations $\dot{x}= x + g\, xy\quad \dot{y}= 1-2x^2-g\, y^2$ where g as parameter.but I don't get any curve on display. Plz help me
0
votes
2answers
89 views

Plotting the solution of a Chini differential equation

In DIFFERENTIAL EQUATION SOLVING WITH DSOLVE by D. Kapadia, there is a Chini differential equation : sol = DSolve[x'[t] == 5 x[t]^4 + 3 x[t]^(-4/3), x[t], t] ...
0
votes
1answer
122 views

Solving Partial Differential Equations using NDSolve

I'm trying to solve the following partial differential equation: With the boundary conditions: I could use another way to resolve this, like the finite volume method, but after I solve the ...
0
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0answers
109 views
4
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1answer
137 views

Solving 2D Laplace equation for irregular boundaries [closed]

I want to solve Laplace equation in 2D with $x$ and $y$ coordinates with the boundary conditions $V(0,y)=-180$; $V(x,0)=50x-180$; $V(x,6)=50x-180$; $V(453.595-\sqrt{450.05^2 - (y - 3)^2},y)=0$ The ...
0
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0answers
52 views

Mathematica treating a system of 1st order nonlinear ODEs as a system of DAEs

I'm trying to use NDSolve to solve a system of 1st order nonlinear ODEs. The system of equations is way too long to post here, but it is in the canonical form: $x_i'(t)=f_i(t,x)$. My problem is that ...
1
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0answers
98 views

Differential algebra package in Mathematica

Is there any equivalent of Maple's differential algebra package in Mathematica? In particular, the Rosenfeld-Groebner algorithm has been implemented?
0
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2answers
89 views

NDSolve with CUDALink

I am solving a system of non linear differential equations. The time needed to solve them is quite long and I would like to shorten it. Is it possible to send the NDSolve command to be solved by the ...
2
votes
2answers
75 views

Slow evaluation of Recurrence plot data from NDSolve: Performance Tuning

I am trying to use a recurrence plot to pinpoint the location when a system re-visits a previous point in its phase portrait. The system (a thin liquid film) is governed by a non-linear differential ...
1
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1answer
62 views

ParametricPlot3D shows an empty box

I'm trying to visualize numerical solution of 4 differential equations (these are the coordinates of a wave function in a quantum mechanical system): ...
8
votes
2answers
271 views

Finite difference method not converging to correct steady state or conserving area?

I am working with the following PDE, which is an advection-diffusion type equation. It describes the movement of a fluid-fluid interface inside an annulus of inner radius $R_1$ and outer $R_2$ under ...
1
vote
1answer
103 views

Not getting the correct solution of a second order ODE [closed]

This is the original question My code is ...
0
votes
0answers
50 views

Help in controlling NDSolve

I have a system of PDE's with initial and boundary conditions I'm solving using NDSolve. There is one term in the system (v) ...
3
votes
1answer
52 views

Solving biharmonic equation with Mathematica

I would like to solve a biharmonic equation in polar coordinates of the form: $\Delta \Delta \Phi[r,\theta] = r^i cos(j \, \theta) \quad i,j \, \epsilon \, \mathbb{N}_0 $ I know that a solution for ...
7
votes
1answer
86 views

NDSolve how to monitor shooting method iteration?

here is a shooting method solution right out of the docs: ...
1
vote
1answer
70 views

Stiffness problem in an NDSolve system. StiffnessSwitching does not help?

I'm trying to solve an ODE system with the NDSolve method. This my ODE system, with the BC and the functions V and dV defined: ...
0
votes
0answers
56 views

Saving the result of a NDSolve

I have solved this diff equation (with no problems): ...
2
votes
1answer
55 views

Problem using Nintegrate and NDsolve

I am going to use Nintegrate to integrate the result of NDsolve and also a Table. How I can ...
7
votes
1answer
80 views

Issuing with ParametricNDSolveValue

I am having a problem with ParametricNDSolveValue[] . let me start with a simple example. Considered following example with constant parameter $a$. ...
2
votes
3answers
113 views

How to integrate numerically the product of result of NDsolve? [closed]

I am going to integrate the product of the results of NDsolve, in fact If x and y are the results as interpolating function, How I can integrate x*y numerically? <...
0
votes
1answer
37 views

NonlinearModelFit error: the function value is not a list of real numbers with dimensions {101} at {a,k,m0} = \ {1.,1.,1.} [closed]

So I'm trying to find a sigmoidal fit for my numerical solutions of these two ODEs but I keep getting an error and I don't know how to get around it. Here's my code: ...
1
vote
1answer
132 views

To deal with infinity in NDSolve

Edit: According to Michael E2's comments, I did a few trail and error, and modify the question so that it uses exactly the same expressions I am having difficulties....
0
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2answers
117 views

Solving a set of nonlinear equations

I am trying to setup and solve a set of nonlinear equations. I keep getting an error. Here is my problem: ...
6
votes
1answer
122 views

How to numerically solve a 1D time-independent Schrödinger equation for two interacting particles

Solving the 1D single-electron time-independent Schrödinger equation has been demonstrated using NDEigensystem here. There, the single-electron Schrödinger equation ...
0
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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<...
0
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0answers
67 views

Nonlinear coupled equation (heat equation with source term)

I modeled simple chemical reaction-diffusion equation in spherical region $0\le r\le L$ $${\partial T\over\partial t}={{1\over r^2}{\partial\over \partial r}(r^2{\partial T\over \partial r})+qACexp(-...
0
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0answers
59 views

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}} ...
0
votes
1answer
65 views

Error message when running NDSolveValue

I am trying to solve a set of differential equations but keep getting an error. See message below "NDSolveValue::ndnum: Encountered non-numerical value for a derivative at t=0" The system that I ...
2
votes
2answers
127 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/...
2
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3answers
130 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
-2
votes
1answer
68 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 ...
1
vote
2answers
86 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? ...
2
votes
2answers
262 views

Ion motion in uniform axial magnetic field and radial electric field [closed]

I'm trying to model an ion's 3D motion in a constant/uniform axial magnetic field and a radial electric field (similar to a cylindrical magnetron, but two positive parallel center electrodes offset by ...
0
votes
0answers
36 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
votes
1answer
47 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 ...
8
votes
2answers
130 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 ...
0
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2answers
59 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. ...
0
votes
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.
3
votes
1answer
172 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
51 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
205 views

How to pass arguments in NIntegrate and NDSolve

I am solving PDEs with NDSolve and NIntegrate, but I do not know how to pass arguments correctly. My orignial code is very ...
0
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1answer
119 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 ...
0
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0answers
58 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
53 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: ...
1
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0answers
110 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. ...
2
votes
2answers
67 views
1
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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 ...
0
votes
1answer
61 views

Diffusional equation [closed]

I am still new to Mathematica. I'm trying to solve a diffusional equation ...
0
votes
1answer
58 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},...
0
votes
1answer
56 views