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

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8 views

Infinite Expression Error NDSolve

I'm trying to figure out why I am consistently getting an infinite expression error when I'm trying to solve this DE using NDSolve. Any help will be appreciated. ...
0
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0answers
17 views

NDSolve There are fewer dependent variables, {V[S,t]}, than equation

I am trying to solve the BlackScholes PDE for Barrier option. It works fine for european barrier, but errors out on american boundary condition ...
2
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1answer
112 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
9
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1answer
695 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
0
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0answers
40 views

PDE with Laplacian time derivative term

Using Mathematica 9 I am trying to solve the 2D PDE: c1*Laplacian[-u[x,y],{z,y}] + c2*D[Laplacian[-u[x,y],{x,y}]] == 0 (Eq.1) with time-dependent Dirichlet ...
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1answer
37 views

NDsolve with discontinuous non-numeric PDE coefficients

I want to solve the heat diffusion equation with variable thermal conductivity. So I have the following code ...
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0answers
27 views

NDSolve : Solve a single variable-coefficient ODE as series of constant-coefficient ODEs

I have a manipulator equation of the form: $M(q){q''} + C(q,q')q'+G(q) = {0}$ where $M, C$ are $6$ x $6$ matrices, and $G, q$ are $6$ x $1$ vectors and $q$ a function of time. I would like to ...
0
votes
1answer
49 views

Obtain constant from DSolve [on hold]

I need to extract constant C[1] from expression which I get when solve equation. i.e. DSolve[y'[x]==1/(2x),y[x],x] In result Mathematica gives me this one ...
6
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2answers
147 views

Reject diverging solution of NDSolve

I'm trying to numerically simulate a spring system with complex stiffness. In essence systems of the form $x''(t)+ (a+ ib) x(t)=0$ For this simple example an analytic solution is easy to find. The ...
4
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1answer
133 views
+50

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) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
1
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1answer
114 views
0
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1answer
53 views

Evaluate NDSolve within NDSolve

So I am attempting to solve a differential equation which includes a differential equation (i am not sure if this why my code is giving problems). I am pretty sure that everything is as its supposed ...
1
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0answers
33 views

DSolve -> no results

I am trying to solve a system of differential equations. ...
0
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1answer
76 views

How to solve the following fourth order partial differential equation including Laplacian

I wish to solve the following fourth order partial differential equation including Laplacian with the boundary conditions with the initial conditions ...
0
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1answer
135 views

Solving differential equation with initial conditions

I want to solve the following differential equation with initial conditions: ...
2
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0answers
73 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
2
votes
1answer
54 views

Error accumulation in NDSolve?

I'm trying to solve this system of ODEs numerically: $$\vec{Q} = \vec{P} \times \vec{Q}$$ where vectors $\vec{P}, \vec{Q}$ have 3 components: $$\vec{Q} = \left( Q_1, Q_2, Q_3 \right) $$ $$\vec{P} = ...
0
votes
2answers
87 views

Problem with NDSolve: derivative interpreted as square [duplicate]

I am using Mathematica 9, and trying to solve a very easy differential equation with NDSolve. The code I have is s=NDSolve[{y'[x]==y[x],y[0]==1},y,{x,0,1}] but I ...
0
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0answers
31 views

steady state of coupled partial differential equations

I need to solve coupled differential equations(occur regularly in Phase field theory), \begin{eqnarray} \tau \frac{\partial \varphi}{\partial t} &=& W^2\frac{\partial^2 \varphi}{\partial x^2} ...
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0answers
43 views

How to use NDSolve to solve the system of differential equations? [on hold]

Reference: Mathematical model for HIV/AIDS with complacency in a population with declining prevalence from http://downloads.hindawi.com/journals/cmmm/2006/471467.pdf I found the differential ...
0
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0answers
58 views

NDSolve Syntax Error- 29 simultaneous differential equations [on hold]

Please note that I do not need a detailed solution specific to the equations, but rather a general way to fix the error. I am trying to solve 29 simultaneous differential equations in Mathematica ...
5
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0answers
76 views

Compiling FoldList implementation for RK4

Original I'm looking to write an integrator for a function of two variables. Here is my implementation for the RK4 update rule using FoldList. ...
11
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2answers
240 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 ...
10
votes
1answer
395 views

Inconsistent results of second derivative of inverse fourier transform

I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = \frac{1}{\alpha^2}\frac{\partial u(x,t)}{\partial t}$$ with Mathematica 9. Then solve ...
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0answers
43 views

ParametricNDSolveValue has a problem with complex numbers

Edited: I have simplified the example compared to before and narrowed the problem down a bit. I would like to use ParametricNDSolveValue as function for data ...
-1
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0answers
26 views

Plot How to plot dV/d(lnJ) [closed]

I measured I-V characterization, so I've got their data. But sometime I want to plot dV/d(lnJ) curve with my data. Can someone help me? How to plot dV/d(lnJ), J is current density.
0
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1answer
71 views

Solving non-linear ODE analytically in mathematica [closed]

I would like to solve the following differential equations $${dx\over dt}=\beta x-{{(C-x)^2}\over 4k} ,t\in[0, T]$$ where $\beta$,$C$ and $k$ are constant values. Also, the folowing terminal ...
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1answer
74 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 ...
0
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0answers
63 views

How do I solve a system of PDE with a Dirichlet boundary condition and piecewise condition Initial?

How do I solve the system of PDE with boundary value like this and initial conditions piecewise Please help me to find a solution in a Wolfram Mathematica program. I have several times ...
3
votes
3answers
132 views

Trouble with differential equation

I tried to solve this differential equation: $$\epsilon y''(x)+xy'(x)=-\epsilon \pi^2 \cos(\pi x)-\pi x\sin(\pi x)$$ with boundary conditions: $y(-1)=-2, \space y(1)=0$. If we take $\epsilon=0.1$, ...
1
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4answers
127 views

Why can't Mathematica DSolve my equation? [closed]

I am trying to solve $\begin{cases} v(t) = A \cdot e^{kt} \\ v(t) = s'(t) \\ s(0) = 0 \\ v(0) = A \\ v(6000) = 299792458 \\ s(6000) = 2.37 \cdot 10^{16} \end{cases}$ for $A$ and $k$. But neither of ...
3
votes
1answer
86 views

Use FEM Solver for System of Nonlinear PDEs with Nonlinear Coefficients - Reaction-Diffusion

I am trying to solve a complex transient reaction-diffusion problem numerically in 2D. Let's take a simple system to start, say $$ A+B\rightarrow C \\ C \rightarrow A+B $$ with reaction rate $k_1$ ...
2
votes
2answers
124 views

Steady State Numerical Solution of Heat Diffusion Equation in 2D

I'v been trying to solve for the steady state of the heat diffusion equation numerically but I cant seem to get it to work. My code is ...
2
votes
3answers
126 views

Why does DSolve return two solutions for my ODE?

I wanted to solve the differential equation: $y’ = (1+2x)\sqrt{y}$ with $y(0) = 1$. It can be done by hand, and to check my answer I typed the following in Mathematica ...
8
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1answer
969 views

Controlling the time step in NDSolve?

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out ...
0
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0answers
61 views

Retrieving forthcoming step size from NDSolve

I'm solving a system of ODEs with a random component, which changes at each calculation step and depends on the step size. So I'm trying to realize something like this: (1) size of the forthcoming ...
2
votes
1answer
85 views

NDSolve-Problem (Calculating field lines)

I want to calculate the field lines of a quite nasty vectorfield. In general the method works fine - except, one of the components of the VF gets 0 - then NDSolve ...
1
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1answer
159 views

Modeling a stellar atmosphere

I'm trying to model a stellar atmosphere using Mathematica. Basically I'm working in a physical and chemical model which combined should give me a profile of the chemical abundance in the atmosphere. ...
2
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0answers
41 views

NDSolve returns asymmetric solution to a symmetric equation

I am trying to find the potential of a conducting cylindrical electrode by solving the Laplace's equation. Both, the boundary conditions and the equation are symmetric w.r.t. the change $r\to-r$. ...
3
votes
2answers
110 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 ...
0
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0answers
62 views

Boundary value problem time imaginary method [closed]

I want to solve the following equation using the time imaginary method. $\quad \quad -y''(n)+n^2\,y(n)-{\rm abs}(y(n))^2\, y(n)=M\,y(n)$ where $M$ is an eigenvalue and with boundary conditions ...
2
votes
1answer
186 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
5
votes
4answers
708 views

DSolve not finding solution I expected

Try to solve the following ODE via DSolve $$ \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. $$ The ...
4
votes
1answer
60 views

WhenEvent used in a PDE to output independent variable

I want to use WhenEvent with a PDE after it has reached steady state. I'm posting a system of 2 equations (my real system has 6) and I'm solving the advection-diffusion-reaction 2nd order PDE. First ...
2
votes
1answer
111 views

How I can make the StreamPlot of this differential equation?

I need the StreamPlot of this differential equation but I don't know how. dp/dt = 0.4 p(1 - p/30), 0 <= t < 5 and 0.4 p (1 - p/30) - 0.25 p, t > 5
1
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1answer
93 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. ...
3
votes
1answer
91 views

Smoothing a unit step function

I want to smooth a unit step function for use in NDSolve so this function is a smooth function of time (t). How can I do the ...
4
votes
1answer
125 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 ...
2
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1answer
280 views

Smoothing a single rectangular pulse in NDSolve

Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin. I am looking for a smooth function that looks almost exactly the same as the square wave ...