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

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-3
votes
1answer
108 views

Transform differential equation to get equilibrium position [closed]

I would like to determine the equation in the equilibrium position. eq = 1/2 g l m Cos[θ[t]] == J (θ^′′)[t] ...
1
vote
0answers
73 views

ParametricNDSolveValue over a region

I'm getting the following behavior I don't understand when using ParametricNDSolveValue over a region. You can reproduce the behavior considering Poisson's equation ...
0
votes
0answers
53 views

Multidimensional Fourier PDE solution and and exact solution are scaled by $(2 \pi)^{2}$

I'm solving a partial differential equation (Stokes equation) in a periodic domain in three dimensions with fourier transforms. I'm using Fourier[] mathematica routines to perform the discrete ...
0
votes
0answers
122 views

Divergence in the initial value problem solved by Ndsolve

here is to ODE I need to solve: ...
0
votes
0answers
120 views

To find a surface with constant Gauss curvature

Please help me use NDSolve to find a surface with constant Gauss curvature $K$ in Cartesian coordinates. I have no previous experience with such differential ...
0
votes
0answers
61 views
0
votes
0answers
28 views

Solving an inhomogeneous partial differential equation [duplicate]

Here is my inhomogeneous partial differential equation: $$ \left ( \frac{\partial^2 }{\partial \rho^2}-\frac{1}{\rho} \frac{\partial }{\partial \rho} + \frac{\partial^2 }{\partial z^2}\right ) \psi= ...
1
vote
1answer
216 views

Particle motion with discrete values for the potential

Sorry if the question seems trivial, but I am new to physical simulations in Mathematica. I have a numerical estimation of an electric potential $V(x)$ in 3D, to be more precise I have a matrix ...
1
vote
1answer
179 views

NDSolve`Reinitialize start from previous solution but with different boundary conditions

I am solving a set of coupled partial differential equations (some variation of a 1 dimensional compressible fluid flow). I want to solve the equations (NDSolve, this works fine) but then continue ...
2
votes
2answers
201 views

Overdetermined System of PDEs

EDIT: Just to clarify a large part of my question is whether there is a way to make Mathematica solve a system with more equations than independent variables (so a system that is overdetermined but ...
1
vote
1answer
124 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
votes
1answer
76 views
1
vote
0answers
68 views

Errors when thickness is reduced solving 2D cylindrical heat conduction equation

I am trying to solve the heat conduction equation in cylindrical coordinates with a defined heat generation within the volume (a thin disk, with different heat flux BC top and bottom). The problem is ...
0
votes
1answer
83 views

Differential equations DSolve constant issue

After using DSolve to a set of differential equations, three constants arise. They are C[1], C[2] and C[21]. I have checked thoroughly that there are no C[3], C[4],....C[20]. It is quite mysterious to ...
1
vote
1answer
268 views

How to impose normalization condition (not initial condition) on DSolve or NDSolve?

I have a set of differential equations (or DAEs): $\begin{cases} 5x_{2} + 3x_{4} + 3x_{5} = \frac{dx_{1}}{dt}\\ 5x_{1} + 5x_{2} + 5x_{3} + 3x_{4} + x_{5}= 0\\ 3x_{2} + 3x_{4} + 10x_{5} = \frac{dx_{3}}{...
4
votes
2answers
195 views

Problem with ParametricNDSolve

i have a strange problem with ParametricNDSolve. Given the sistem of differential euqations ...
0
votes
1answer
43 views

Numerical error in DSolve [duplicate]

I'm solving the 1D Poisson equation and am getting some funky numerical artifacts in the solution. ...
1
vote
1answer
113 views

DSolve with Absolute Value

When playing around with DSolve, I enter the following: DSolve[{Derivative[1][y][x] == x + Abs[x]*y[x]}, y[x], x] The output is: $$y(x)\to e^{\frac{1}{2} (x \...
0
votes
1answer
105 views

Method that combine LinearSolve and Dsolve for a set of differential equations?

I have a matrix for example: $\begin{bmatrix} 0 & 5 & 0 & 3 & 3\\ 5 & 5 & 5 & 3 & 1\\ 0 & 3 & 0 & 3 & 10\\ 1 & 3 & 2 & 3 & 10 \\ 1 &...
1
vote
1answer
100 views

System of differential equation with delay

I try to solve this differential system with delay: ...
0
votes
2answers
631 views

Lotka Volterra Equation Plotting

So I have a basic Mathematica assignment where we need to numerically solve a Lotka-Volterra predator-prey population equation. So far I have managed to come up with this ...
3
votes
5answers
420 views

Taylor series without expanding factorial in denominator

A Taylor series is produced with the following code: ...
4
votes
1answer
522 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by <...
6
votes
1answer
141 views

What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
4
votes
1answer
205 views

Solving PDE with Condition on Inside of Region

I'm trying to figure out how to use NDSolve to numerically solve PDEs where some internal values may be specified on the region of the solution. An example, which I picked from a textbook, is solving ...
0
votes
1answer
45 views

What function is the best for solving differential equations? [closed]

dy/dt = -y^2, what is the best function to solve this equation?
4
votes
1answer
415 views

NDSolve grid refinement for PDEs

I am experiencing trouble when trying to solve a PDE for various parameter values within mathematica: The PDE in principle can easily be solved numerically, however the stepsize of the spatial ...
1
vote
1answer
491 views

Integral Curve Question using Contour Plot

The ODE $$(xy-2)+(x^2-xy)y'=0$$ is NOT an exact differential equation. However, if I multiply both sides by an integrating factor $\mu=1/x$, the resulting equation $$\left(y-\frac2x\right)+(x-y)y'=0$$...
0
votes
0answers
94 views

DSolve gives back input (coupled ODEs)

I'm trying to solve a system of coupled ODEs, however I keep getting back the input whenever I try to solve with DSolve. The variables I'm solving for are complex. Here's what I have : ...
2
votes
2answers
46 views

Filling a region defined by a reduce command

I'd like to shade the region defined in the xy-plane produced by this code: ...
1
vote
0answers
187 views

Simulate a polygon bouncing with collision detection inside a circle/polygon

Simulate a polygon bouncing with collision detection inside a circle/polygon. the example can be see in help page by searching WhenEvent; ...
0
votes
1answer
130 views

PDE raises NDSolve::ntdvdae, then kernel quits

In a related question, the SolveDelayed->True option seemed to solve the problem. SolveDelayed is not a valid option in M10 (...
9
votes
2answers
370 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
4
votes
1answer
165 views

OutputResponse in V9 vs V10

Bug introduced in 10.0.1 and persisting through 10.2 or later I have same code that works in version 9.0.1, but not in version 10.0.1.0 (according to @Sektor, it works in 10.0.0.0, too). ...
-1
votes
1answer
155 views

Small mismatch in theoretical vs MMA solutions of a damped harmonic oscillator differential equation

I solved the differential equation $$ \ddot y + 0.43 \dot y + y =0.1 \cos(2x), \quad y(0)=1,\ \dot y(0)=1 \quad(0) $$ using both the theoretical results from wikipedia and using MMA (I also tested ...
1
vote
1answer
114 views

How can I simplify the result of a differential equation by using my own defined expressions? [duplicate]

I want to solve the following differential equation with mathematica: α β * w''''''[ξ] + ( 1 + α - p ) * w''''[ξ] + p/β * w''[ξ] = 0 The answer seems at ...
1
vote
1answer
280 views

Solving a nasty partial differential equation

I have a differential equation that I would like to solve numerically in the region $z \in [0,L]$ and $t \in [0,t_{max}]$: $$ \partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t), $$ ...
1
vote
1answer
115 views

How to get the raw data of solutions of partial differential equation in mathematica

I am using NDSolve command of mathematica solving a very complicated partial differential equation (two independents "t" and "x", three master variable "u", "v", "w"). Each time I solve it, it takes ...
-1
votes
1answer
94 views

Third-order ODE with NDSolve

I would like to use NDSolve to draw the integral curve of a third-order ODE ...
0
votes
1answer
236 views

NDSolve with initial condition: initial conditions did not evaluate to an array of numbers of depth 1(for 1D) or 2 (for 2D) on spatial grid

I have the following naive code to solve a PDE in two spatial dimensions (x,y) with periodic boundary conditions: ...
1
vote
1answer
152 views

DSolve for Second Order Differential

I have an equation y''[t] + w^2*Sin[y[t]] == 0 So I'm using DSolve like this: ...
0
votes
1answer
67 views

Simplifying an answer returned by DSolveValue

Consider the IVP: $$x'=\frac92-\frac{x}{300+2t},\quad x(0)=0$$ Working the solution by hand, the answer is: $$x(t)=450+3t-\frac{4500\sqrt3}{\sqrt{300+2t}}$$ Entering code and then attempting to ...
7
votes
1answer
172 views

Eliminating NDSolve Instability

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5
votes
5answers
388 views

Plot all curves in a table with a single color

I want all of my solutions in a table to be the same color. My attempt: ...
1
vote
3answers
404 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 ...
5
votes
2answers
892 views
0
votes
0answers
97 views

Selecting values over lists for discrete inputs in NDSolve [duplicate]

I'm currently trying to simulate a step response in a simple tank system with NDSolve. I would like it to start at say time 2 (the precise time is not important). ...
2
votes
0answers
208 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
1
vote
1answer
58 views

Variables within functions within DSolve

Hi I am just beginning to learn Mathematica and this is my first time I have been exposed to any type of coding. I am encountering a problem in a basic physics problem. For example we are always ...
2
votes
2answers
262 views

Too high differential order in boundary conditions?

The following boundary value problem has a unique solution: $$ \begin{cases} x''-x=0\\ x''(0)=0\\ x(1)=1 \end{cases}\\ \text{General solution: } x=c_1 \sinh{t}+c_2\cosh{t}\\ \text{Solution for BVP: } ...