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

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0
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0answers
84 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
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1answer
56 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 ...
0
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1answer
219 views

Help solving the following non-linear differential equation

After spending several hours exploring different options, I still couldn't not figure out how to solve the following differential equations. Any suggestions would be highly appreciated. ...
1
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1answer
93 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
3
votes
1answer
110 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: ...
1
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1answer
60 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
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1answer
99 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
6
votes
2answers
708 views

StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
0
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0answers
56 views

Linear system of stochastic differential equations

I want to solve linear system of differential equations of the following form $$X'[t] = M.X[t] + R.X[t]*\lambda[t]$$ where $X[t]$ is a vector of coefficients I want to have at time $t$, $M,R$ are ...
4
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2answers
91 views

Problem with ParametricNDSolve

i have a strange problem with ParametricNDSolve. Given the sistem of differential euqations ...
0
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1answer
64 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
80 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} = ...
0
votes
1answer
76 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 ...
0
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1answer
35 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
73 views

System of differential equation with delay

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

System of ODEs with Parameters

FYI: I am new to Mathematica so my questions are probably pretty amateur. I am attempting to write a code to numerically solve the system of equations: {dp/dt= ap-bpx {dx/dt= spx-yx where t is the ...
0
votes
1answer
106 views
1
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1answer
71 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 ...
0
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0answers
45 views

Problem of WhenEvent in using variable updated in Event

equation1: value[inside RotationTransform] is a constant ...
3
votes
5answers
255 views

Taylor series without expanding factorial in denominator

A Taylor series is produced with the following code: ...
3
votes
1answer
345 views
1
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0answers
113 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; ...
-1
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1answer
439 views

Problem with #1's in DSolve

I've entered the following functions into my notebook, but the solution to them contains #1's that I can't seem to make any sense of. The functions are: ...
0
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1answer
45 views
24
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1answer
750 views

Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
3
votes
1answer
102 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
106 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 ...
1
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2answers
43 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: ...
9
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2answers
206 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. ...
0
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1answer
57 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 ...
-1
votes
1answer
135 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
135 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 $t \in [0,t_{max}]$: $$ \partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t), $$ ...
0
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1answer
61 views

Third-order ODE with NDSolve

I would like to use NDSolve to draw the integral curve of a third-order ODE ...
1
vote
1answer
67 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: ...
3
votes
1answer
209 views

Boundary sphere partial differential equation

I am trying to solve partial differential equation in spherical coordinates $(\theta,\phi)$,but I don't know how to properly include boundary conditions of $\theta$. For $\phi$ it is periodic, but ...
1
vote
0answers
84 views

System of differential equations [closed]

I have to solve the following system of two differential equations with certain parameters inside which I just put them together for simplicity and called them t: ...
0
votes
1answer
54 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 ...
4
votes
5answers
253 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: ...
0
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3answers
85 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 NSolve and Manipulate. Based on those, I wrote the following code, solving my system of equations: ...
0
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0answers
64 views

Selecting values over lists for discrete inputs in NDSolve

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). ...
4
votes
1answer
255 views

Differentiating ParametricNDSolve solutions

Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
2
votes
0answers
62 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
42 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
141 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: } ...
2
votes
2answers
59 views