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

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0answers
53 views

Linearization of differential equations at first order

Currently, I migrate my Maple Code to Mathematica code. On a part linked to linearization, I meet some difficulties. In fact, i try to linearize some differential equations around an equilibrium ...
0
votes
0answers
52 views

Generate a small random disturbance on a flat surface for NDSlove

I want to generate a small random perturbation on a flat surface defined on a square domain, e.g. 1 + 0.05 rand(x,y), which can be used as initial condition with periodic boundary conditions in ...
1
vote
2answers
87 views

Linearization of differential equations

I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the ...
0
votes
1answer
44 views

Unable to break out of two Do loops

I wrote a mathematica program to solve one dimensional schrodinger equation for particle in box model with zero potential. I used two do loops to achieve the task. The inner do loop will solve ...
0
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1answer
81 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
-1
votes
1answer
67 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
100 views

How to change the form $A\cos \omega t + B\sin \omega t$ into the form $\sqrt{A^2+B^2}\cos(\omega t-\phi)$ [duplicate]

I'm preparing notes for teaching next week's class in differential equations. My hand calculation solution of $$y''+192y=0, y(0)=1/6, y'(0)=-1$$ is $$y=\frac16\cos 8\sqrt3 t-\frac{\sqrt3}{24}\sin ...
0
votes
1answer
45 views

Use ParametricNDSolve with Plotting

I am attempting to solve a differential equation of the form $$ \frac{dx}{dt}=ax+by \\ \frac{dy}{dt}=cx $$ with parameters $0<a<1$ and $a,b,c \in \mathbb{R}$. I am able to use NDParametric ...
0
votes
3answers
84 views

How to define a function

How can I define a function which depends on a function of x? Something like this f[u[x]_,u[x]']= u[x]' + a [x] u[x] +b[x] I think I wasn't enaugh clear. If I ...
0
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0answers
47 views

How could I solve following equation? [closed]

I am quiet new to Mathematica. I was wondering if someone could give me some pointers towards solving an equation of this sort: Here is what I know: The change of temperature, T (Celsius) with ...
-2
votes
1answer
59 views

Transform differential equation to get equilibrium position

I would like to determine the equation in the equilibrium position. eq = 1/2 g l m Cos[θ[t]] == J (θ^′′)[t] ...
1
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0answers
35 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
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0answers
29 views

NDSolve — using a PDE solution in another PDE

My problem is to use the numerical solution of a PDE as a function appearing in another PDE. Here is the code solving the first PDE (heat equation in a domain) : ...
0
votes
0answers
24 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 ...
-2
votes
0answers
24 views

Assigning values to constants after solving a set of differential equations [closed]

I solve the equations of 40 variables. Three of the equations are differential equations. Therefore, it is a set of differential algebraic equations. This is the following set of equations: ...
0
votes
0answers
54 views
0
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0answers
77 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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0answers
37 views
1
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1answer
48 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 ...
0
votes
0answers
31 views

DSolve returns unevaluated, showing some the equations have evaluated to True [closed]

Okay so I looked around everywhere and I just don't get it, this is what happens when I try using it to solve a system of linear equations: I'm probably doing something extremely stupid here, but ...
0
votes
1answer
36 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 ...
1
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1answer
91 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
votes
0answers
34 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 ...
0
votes
1answer
58 views
0
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1answer
59 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
58 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} = ...
3
votes
2answers
64 views

Problem with ParametricNDSolve

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

Numerical error in DSolve [duplicate]

I'm solving the 1D Poisson equation and am getting some funky numerical artifacts in the solution. ...
0
votes
1answer
72 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
69 views

System of differential equation with delay

I try to solve this differential system with delay: ...
0
votes
0answers
33 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
0answers
63 views

Implicit/Backward Euler method

I'm trying to solve (and plot) a differential equation using Explicit Euler method and Implicit Euler method. The Implicit method worked out jst fine but I have problems with Implicit one... I made ...
2
votes
5answers
213 views

Taylor series without expanding factorial in denominator

A Taylor series is produced with the following code: ...
0
votes
0answers
40 views

Problem of WhenEvent in using variable updated in Event

equation1: value[inside RotationTransform] is a constant ...
1
vote
1answer
62 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 ...
3
votes
1answer
102 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: ...
0
votes
1answer
43 views

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

dy/dt = -y^2, what is the best function to solve this equation?
3
votes
1answer
68 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
83 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
vote
2answers
41 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: ...
0
votes
0answers
86 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
48 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
189 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. ...
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votes
1answer
127 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
65 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
99 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
votes
1answer
55 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
81 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: ...