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

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2
votes
0answers
68 views

DSolve solution of two unknowns

I have one problem with the solution of the system of two differential equations. I waited hours, but Mathematica didn't give me a solution. Is there any way to obtain the results if we suppose that ...
3
votes
1answer
88 views

How to deal with the discontiuity in the solution of NDSolve?

I have a set of differential equations that describe the air temperature dynamics in a heated channel.The problem is that the solution becomes unstable and creates a discontinuity but physically it ...
2
votes
1answer
74 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
0
votes
0answers
39 views

NDSolveValue:dsvar error in a system of non linear differential equations generated using a Table

I have a system of 4 non-linear differential equation, that I generate using Table command. On solving, I keep getting a dsvar error that is not going away. I debugged my code and figured it has to do ...
1
vote
1answer
186 views

error DSolve::dsfun: cannot be used as a function

I tried to solve system of ODEs, but something was wrong. ...
5
votes
2answers
103 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
0
votes
1answer
99 views

How to solve and plot this 2nd order non linear ODE? [closed]

Is this the correct way to plot the solution of this ODE from $(-8, 8)$? $$y'' - (1 - (y')^2)y' + y = 0$$ ...
0
votes
1answer
63 views

NDSolve emitting error message NDSolve::ndnum [closed]

I am trying to solve this system equn1 = ψ'[x] == - Elec[x] equn2 = Elec'[x] == - ((di/ a)^2)[(Exp[ψ[x]] - (x/(xoi*Sqrt[-ψ[x]])))] For that I am using ...
2
votes
1answer
99 views

How to write ODE to standard form?

Package like odepack needs the ODE written in standard form, which means write the high order ODE to first order ODE equations. The steps of converting ODE to ...
0
votes
0answers
41 views

Graphics Plotfield

A number of older books use the command: <<Graphics`PlotField` But Mathematica 10.0.2 says it cannot find it. Now, I know VectorPlot, but I am wondering if ...
2
votes
1answer
106 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 ...
0
votes
1answer
116 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 ...
2
votes
2answers
145 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
55 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
votes
1answer
120 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
81 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
2
votes
2answers
182 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
108 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
0answers
127 views

NDSOlve - 1D wave equation with boundary

I am currently trying to solve the 1D wave equation with Mathematica: $$c^2\frac{\partial u}{\partial x^2}=\frac{\partial u}{\partial t^2}$$ I want to do so for a cantilever with a tip mass: One ...
0
votes
3answers
123 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 ...
1
vote
1answer
135 views

PDE solution does not satisfy Neumann boundary conditions using NDSolve

I am trying to solve the free particle Schrodinger equation in 1D (hbar =1, Energy = 1, mass = 1), But specifying conditions only on x==0: ...
-2
votes
1answer
81 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
vote
0answers
56 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
56 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
38 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
17 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): ...
0
votes
0answers
76 views

Divergence in the initial value problem solved by Ndsolve

here is to ODE I need to solve: ...
0
votes
0answers
88 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
39 views
0
votes
0answers
23 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
78 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
78 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
123 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
111 views

Help with plotting and improving code

I'm trying to solve a coupled DDE. Here is my code ...
0
votes
0answers
77 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
70 views
1
vote
0answers
48 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
70 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
123 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} = ...
4
votes
2answers
102 views

Problem with ParametricNDSolve

i have a strange problem with ParametricNDSolve. Given the sistem of differential euqations ...
0
votes
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
43 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
84 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
80 views

System of differential equation with delay

I try to solve this differential system with delay: ...
0
votes
0answers
46 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
2answers
171 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
285 views

Taylor series without expanding factorial in denominator

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

Problem of WhenEvent in using variable updated in Event

equation1: value[inside RotationTransform] is a constant ...