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

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1
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2answers
43 views

ParametricNDSolve and NDSolve inside Manipulate environment

I have a system of three coupled differential equations that can be pretty readily solved by NDSolve: ...
6
votes
1answer
815 views
0
votes
0answers
57 views

singularity problem in mathematica [duplicate]

$$ \pmb{\beta [\text{b$\_$},\text{c$\_$}]=\frac{4 c-14}{12 b-6 c-9};}\\ \pmb{\alpha [\text{b$\_$},\text{c$\_$}]=\frac{10-4 b}{12 b-6 c-9};}\\ ...
20
votes
2answers
395 views

Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
6
votes
2answers
305 views

Kernel quits without error in NDSolveValue

The crash is fixed in version 10.3 I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
6
votes
1answer
162 views

Long running ToElementMesh with very “large” domains

This is fixed in version 10.3. I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. ...
4
votes
2answers
130 views

Solving parametric ODEs at large parameter values

Question 101668 was not particularly clear and was put on hold for that reason. The author did clarify it a bit, but it seems unlikely that the question will be reopened. Through an exchange of ...
5
votes
2answers
96 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 ...
1
vote
0answers
75 views

How to make a parameter stochastic in a differential equation system with NDSolve?

I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
5
votes
2answers
284 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
7
votes
3answers
195 views

Vector form using NDSolve

Michael E2 wrote a wonderful solution for my question. Now I am considering the system: $$ \begin{align*} x'&=x^2 y,\ x(0)=1\\ y'&=-x y^2,\ y(0)=1 \end{align*} $$ I am wondering how I can ...
3
votes
1answer
35 views

solving large number of linear differential equations

I want to solve a large system of 500 by 500 differential equations such that I have equations such as: Note all the A1, A2 are ...
0
votes
1answer
113 views

how to write this equation In mathematica. where is W is random value either 0 or 1

how to write this equation In mathematica. where is W is random value either 0 or 1. i want to run to certain N=100 I already have ...
1
vote
0answers
75 views

Coupled ODEs with boundary conditions - DSolve Error [closed]

I'm relatively new to mathematica and I can't find the error here. I suspect it has something to do with the fact that vx, vy, vz aren't blue on my mathematica - as in, they already have some assigned ...
6
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
1answer
124 views

Solving systems of equations and derivatives

I am new to Mathematica, and I'm not sure how to solve a system of equations that include differentiation. Given that f and g are differentiable functions: ...
0
votes
0answers
22 views

How to use `DSolve` with y'' and y' in the same argument? [duplicate]

I'd like to solve the differential equation $y''(x)=xy'(x)$ in Mathematica. I'm not sure if it can be solved analytically. This is what I have tried: ...
0
votes
0answers
464 views

Poincare Section of an Hamiltonian

I'm in desire to plot the Poincare Section of a differential equation defined by a hamiltonian system. The hamiltonian is as follow: ...
0
votes
0answers
191 views

How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In ...
3
votes
1answer
65 views

Find an appropriate algorithm for certain type of first order nonlinear PDE

I am trying to solve a first-order nonlinear PDE of the form $$ \partial_t z(t,x) = f(t, x, z(t,x), \partial_x z(t,x)) $$ with the boundary condition $$ z(0,x) = \phi(x) $$ for some finite domain $x ...
3
votes
1answer
145 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} ...
0
votes
0answers
22 views

Iterating with NDSolveValue in a Do-loop [duplicate]

I am trying to get a differential solution to converge. There are two separate time periods that I am solving for and the entire solution is periodic. I want to use the output from one as the input ...
0
votes
1answer
39 views

Error produced when trying to solve ordinary differential equation [closed]

NDSolve[{x0'[t] == -x0[t]*s*x1^2 + s*x1^2, x1'[t] == x1*s*x1^2, x2'[t] == -x2[t]*s*x1^2, x0[0] == x1[0] == x2[0] == 1}, {x0, x1, x2}, {t, 0, 1}]
3
votes
1answer
77 views

I Need help to solve the differential equation below

I tried to solve the equation using the code below, but got a null solution. If you change the values of p for 2 and alpha to -1.99, a smooth and nonzero solution is obtained. But I need to respect ...
0
votes
0answers
339 views

Laplace PDE in a polar coordinate system

I want to solve a Laplace PDE in a polar coordinate system with finite difference method, but I have a problem with boundary conditions at r = 0. Here is what I ...
1
vote
1answer
135 views

Why can DSolve not solve this ODE? [closed]

I wish to solve an equation for the field lines of an electric field. This is the textbook question 1.3.8(a) from D. Dubin's Numerical and Analytical Methods for Scientists and Engineers, Using ...
0
votes
0answers
59 views

Loop Construct with NDSolveValue for Iterative Solution

I can get this code to run but the plots do not depict the solutions that are being evaluated inside of the Do loop. The plots are only showing the initial ...
0
votes
0answers
481 views

How to apply Robin boundary condition in Mathematica

Robin condition is the boundary condition which combines the Dirichlet and Neumann condition at the same boundary. For example: At the boundary x = 0 to ...
0
votes
0answers
99 views

System of differential equations - solving for a constant

I will reformulate my question in the hopes it will be more intelligible. First, I defined the functions: ...
1
vote
1answer
67 views

How can I combine NIntegrate with NDSolve?

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
1
vote
0answers
69 views

Problem setting boundary conditions with NDSolve

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu ...
4
votes
1answer
263 views

Mathematica 10.3 Dsolve solving 2D diffusion PDE

I tried to use Mathematica 10.3 DSolve to solve 2D diffusion PDE with Dirichlet boundary conditions. But it seems not working. Could anyone help check the code? ...
2
votes
1answer
160 views

How to solve $x' = A\cdot x$? [closed]

I want to solve this equation x' = A x in which x' is a 1*18, ...
2
votes
0answers
84 views

Bypassing a Singularity

I am having trouble trying to solve an ODE that has a singularity when the function M[x]=1. Basically the denominator has ...
0
votes
0answers
72 views

DifferentialRoot

I want to obtain y(x) of following answer with Mathematica: and my code is ...
0
votes
0answers
34 views

Why does the assignment of values to coefficients make a difference to the completion time of DSolve?

I hope to solve the following DAE equations using DSolve, (simplified example, may not be solvable): ...
2
votes
1answer
151 views

Mysterious Difference in Equation Formulation for NDSolveValue and NDEigensystem

I have taken a standard equation from Mathematica help from here for a stress operator. I have also formulated the equivalent equations from engineering texts. When I compare the two equations Using ...
6
votes
1answer
221 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) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
0
votes
0answers
78 views

How to simplify a messy integrand by integrating by parts

I have a function x[t] and a messy integral over t, containing x[t], ...
0
votes
1answer
54 views

Shooting method — why is NDSolve giving me an error message?

I am currently trying to write a code to implement the so-called shooting method (I've given a brief description of it below, for those unfamiliar) for second order ODE's in the form ...
2
votes
1answer
90 views

Finding terms of the perturbation solution

I've got a task to find first three terms of the perturbation series solution to: $$y' = 1 +(1+\epsilon)y^2,\quad y(0)=1, \quad t > 0,$$ for a small $\epsilon$. I am supposed to use Mathematica ...
1
vote
1answer
104 views

Time-dependent pde with periodic boundary conditions - NDSolve gives incorrect results

I'm trying to solve very simple differential equation with perdiodic boundary conditions and non-constant initial condition, however the results I'm getting don't seem to be correct. Here's my code: ...
4
votes
1answer
77 views

DSolve returning InverseFunction while I believe the answer isn't so complicated

I was trying to solve the following differential equation: $$A'(y)^2 = -\frac{1}{l^2} e^{-2A(y)} + \frac{1}{L^2}.$$ I know that one possible answer is $$A(y) = \log\left( ...
0
votes
3answers
167 views

About a simple differential equation

Just a simple differential equation.Even we can hand to solve it.But the Mathematica give a error. ...
0
votes
1answer
53 views

How can I solve NDSolve with a parameter?

I'm a new user and I have no idea how to solve the equation with a parameter by using NDSolve. For example consider following differential equation (DE): ...
4
votes
1answer
86 views

StreamPoints adding extra information

Why doesn't the red line start precisely at the defined point $(0, 2)$ and go off to infinity? My initial condition is $(0, 2)$ and I only want to see where that trajectory goes off to. ...