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

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2
votes
2answers
64 views

FEM: This is not a polynomial error

Executing the program below I get the This is not a polynomial error message. I don't have an idea why I am getting this -- any suggestions ? ...
3
votes
3answers
70 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
votes
1answer
60 views

Nonlinear boundary value problems for fourth order ordinary differential equations

I am trying to solve a set of equations which are fourth order equations. I want to get the value of w ...
0
votes
1answer
86 views

Solve a differential equation using the power series method

I used the power series method to solve the differential equation y’’+y=0 with y[0]=0 and y’[0]=1 using the following code. In this code “y” is considered as “y = Sum[c[i] x^i, {i, 0, n}] + O[x]^(n + ...
0
votes
1answer
78 views

Solving a simple linear differential equation does not work as advertised [on hold]

I have been following examples in an introduction to Mathematica. But the following example regarding a linear differential equation does not work: ...
0
votes
0answers
64 views

PDE with Laplacian time derivative term

Using Mathematica 9 I am trying to solve the 2D PDE: c1*Laplacian[-u[x,y,t],{x,y}] + c2*D[Laplacian[-u[x,y,t],{x,y}],t] == 0 (Eq.1) with time-dependent Dirichlet ...
2
votes
3answers
119 views

Solving a differential equation with NDSolve and plotting it WITH the use of Manipulate

I want to solve, let's say, this differential equation: y'[x]=y[x]^n Given any initial condition (which I might want to manipulate too). I want to plot the ...
1
vote
1answer
37 views

Non-autonomous Dynamical system Sliding mode controller Error

This code is a simulation of a sliding mode controller of a non-autonomous dynamic. When I use ArcTan in input, I receive an error. ...
1
vote
1answer
50 views

Ndsolve problem with Sign

Using Sign(...)] in the formulation of my system of ODEs is causing an error that I don't know how to correct. If I use (...) in ...
2
votes
1answer
474 views

Animated Wave propagation using split operator method

Here is the state of the art: By solving the time-dependent Schrödinger equation, one obtains that the propagated wave function after time step $\Delta t$ can be calculated by applying the ...
1
vote
0answers
72 views

Solution to heat equation with Neumann boundary conditions and lateral heat loss

I am conducting an experiment on heat conduction in a copper rod. To do so I am using a thin copper rod with several temperature probes, then I am going to compare the data with a solution to the heat ...
2
votes
1answer
46 views

Stopping NDSolver at time of error

I am using NDSolver and WhenEvent to solve a system of differential equations. I get this message: ...
2
votes
1answer
90 views

Gradients of the NDSolve PDE solution

I would like to understand, how to obtain gradients of the PDE solution obtained with NDSolve. To be precise let us consider a Laplace equation from one of the examples: ...
1
vote
3answers
141 views

Trouble using Manipulate and NDsolve for coupled ODE's

I'm aware that there are a few threads on the topic of solving coupled ODEs using NDSolve and Manipulate. Based on those, I ...
3
votes
1answer
110 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 $k_1$ ...
5
votes
2answers
237 views
2
votes
1answer
89 views

solve nonlinear equations with NDSolve

I am trying to solve a set of equations with NDSolve. one of them is mg*yg''[t] == NN[t] - kb*yg[t]^1 - cb*yg'[t], When the power of yg[t] is 1 the equations could ...
0
votes
1answer
49 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 ...
1
vote
1answer
762 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
0
votes
0answers
30 views

ParametricNDSolve of differential equation with singularity

I have a differential equation I would like to solve with the ParametricNDSolve. However, the coefficients in the differential equation are singular at a certain value, so sometimes NDSolve crashes ...
2
votes
1answer
79 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
0answers
39 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. ...
3
votes
1answer
72 views

How to control when NDSolve is called inside Manipulate

Let's say I have a function which returns the resulting function of a differential equation solved by NDSolve: ...
2
votes
1answer
113 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
votes
1answer
698 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
votes
1answer
42 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 ...
0
votes
1answer
51 views

Obtain constant from DSolve [closed]

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
votes
2answers
153 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 ...
5
votes
1answer
160 views

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
vote
1answer
121 views
0
votes
1answer
56 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
vote
0answers
36 views

DSolve -> no results

I am trying to solve a system of differential equations. ...
0
votes
1answer
84 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
votes
1answer
135 views

Solving differential equation with initial conditions

I want to solve the following differential equation with initial conditions: ...
2
votes
0answers
75 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 ...
0
votes
2answers
89 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
votes
0answers
35 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} ...
0
votes
0answers
44 views

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

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 ...
5
votes
0answers
81 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
votes
2answers
252 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 ...
2
votes
0answers
44 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 ...
0
votes
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 ...
0
votes
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
votes
0answers
68 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
134 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
vote
4answers
128 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 ...
2
votes
2answers
131 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 ...