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

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0
votes
1answer
21 views

Manipulating of non linear differentials equation

I want to manipulate non linear differential equation x dot= x + g xy and y dot= 1-2x^2-g y^2 where g as parameter.but I don't get any curve on display. Plz help me
0
votes
1answer
37 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] ...
4
votes
0answers
64 views
+50

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 ...
2
votes
1answer
69 views

Solving 2D Laplace equation for irregular boundaries

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
votes
1answer
58 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 ...
2
votes
2answers
57 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 ...
0
votes
0answers
36 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 ...
0
votes
0answers
48 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
votes
1answer
35 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 ...
0
votes
0answers
47 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) ...
1
vote
1answer
60 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): ...
1
vote
1answer
102 views
8
votes
1answer
507 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 ...
1
vote
1answer
67 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: ...
3
votes
1answer
49 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
4answers
745 views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ y_{n}(x):=y_0+\int_{...
7
votes
1answer
81 views
0
votes
0answers
34 views

NDSolve is not giving any result nor any error [on hold]

I am trying to solve a differential equation for $\psi$, but NDSolve is not giving any result nor any error. Please help me. My function is ...
7
votes
1answer
73 views

Issuing with ParametricNDSolveValue

I am having a problem with ParametricNDSolveValue[] . let me start with a simple example. Considered following example with constant parameter $a$. ...
0
votes
0answers
92 views

How can I solve this PDE?

I have been trying to solve this PDE, but Mathematica didn't give me a solution. Here it is: ...
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 ...
0
votes
0answers
91 views

Animating ballistic movement

I was tasked with creating a 3D animation of the movement of a ball through space, while taking into account influences such as the magnus effect, air drag, and rotation. In order for this to happen a ...
13
votes
2answers
266 views

Heat convection differential equations from 1952 - Mathematica “fails to converge”

I am trying to solve a fundamental problem in analytical convective heat transfer: laminar free convection flow and heat transfer from a flat plate parallel to the direction of the generating body ...
0
votes
0answers
51 views

Saving the result of a NDSolve

I have solved this diff equation (with no problems): ...
2
votes
3answers
109 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? <...
1
vote
1answer
91 views

To deal with infinity in NDSolve

I just started to learn to use Mathematica, and was trying to obtain an inverse function. Helpful comments lead to the use of NDSolve, but I encountered the problem ...
0
votes
1answer
35 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: ...
0
votes
1answer
203 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
votes
0answers
39 views

Singularity/Stiff system error

I am after the solutions of the coupled differential equations ...
-2
votes
0answers
79 views

Animating Differential Equations [closed]

I was tasked with creating a 3D animation in Mathematica, which aims to describe the movement of a football through space as it's kicked. There are several differential equations regarding this matter ...
0
votes
2answers
114 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: ...
-1
votes
1answer
128 views
0
votes
1answer
63 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
3answers
128 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 ...
6
votes
1answer
114 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
votes
0answers
64 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(-...
1
vote
2answers
120 views

Discontinuous boundary condition in NDSolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $\cases{ U[0,y,t]=0,& if $0&...
2
votes
2answers
259 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
50 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
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
votes
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/...
1
vote
1answer
44 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
votes
1answer
160 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
vote
0answers
197 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 ...
0
votes
0answers
80 views

Is there a way in which Mathematica 10 can numerically solve a system of PDE with two unknown functions? [closed]

Is there a way in which Mathematica 10 can numerically solve a system of PDE with two unknown functions? For example the system: ∂u/∂x = 2*x*v ∂^2v/∂y^2 = - 2*u - 4*y^2*v with initial conditions: ...
1
vote
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? ...
1
vote
0answers
268 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
votes
2answers
804 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 ...