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

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0answers
14 views

Need help with this integration

I am trying to solve the following differential equation and then integrate the solution by a Gaussian function. The solution to the DE has some Lorentzian functions and Mathematica seems to have a ...
0
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0answers
52 views

Why does my code produce NDSolveValue::ndnum?

I keep getting the error shown below. It appears to be valid, but I am not sure why my I am getting it. ...
0
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0answers
22 views

using numerical value of NDSolve solution [on hold]

I have two differential equations solved using NDSolve ...
0
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1answer
45 views

How can I stop the integration of NDSolve with a condition?

I try to solve a partial differential equation by NDSolve. At some point, I want to stop the integrating by a condition that compares the min value of the function ...
1
vote
3answers
125 views

Higher-order, nonlinear differential equation with Initial Values

I tried to solve for an non-Hookean spring's motion, but the output from Mathematica is weird. It seems that there is inverse functions involved. ...
2
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2answers
113 views

DSolve returning { } when given my ODE

Why does this code return {}? ...
2
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1answer
66 views

Problems with NDSolve and partial differential equations of several variables

Suppose we have the following partial differential equation: $$ 0 = \frac{ \partial w }{ \partial \tau } + \left( w + \sqrt{ h + \beta } \right) \frac{ \partial h }{ \partial \chi } $$ where $w$ = ...
1
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0answers
57 views

Numerical solution to two non-linear coupled differential equations [on hold]

I am trying to solve two differential equations representing the position of an object in space. I have specified arbitrary initial conditions. ...
4
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1answer
72 views

Using NDSolve to solve a system of coupled PDEs

I am trying to solve the Gross-Neveu model in one dimension for a specific soliton initial condition. I am trying ...
5
votes
2answers
153 views

Simplifying general solutions of differential equations (driven harmonic oscillator)

Solving general differential equations in Mathematica usually leads to somewhat unsightly results. As an example, consider the solution of the driven, damped harmonic oscillator: ...
0
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0answers
36 views

Second order nonlinear differential equation [closed]

I want to solve the following second order nonlinear differential equation in Mathematica, but do'nt know how. Please help. ...
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0answers
43 views

No response when try to solve differential equations [closed]

DSolve[y'[x]==x^2,y[x],x] I just tried to solve a simple differential equation by the software, except for a the"Evaluation" blinked once, no response for my ...
2
votes
1answer
81 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
4
votes
1answer
75 views

Drawing disk with coordinates from NDSolve

I have simple Manipulation expression, but continuously getting error Coordinate {x[0.], y[0.]} should be a pair of numbers, or a Scaled or Offset form. I assume that something is wrong with ...
0
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0answers
36 views

Why NDSolve With Orthogonal-Projection Method On Orr-Sommerfeld Equation Does Not Work(?)

I am attempting to solve the Orr-Sommerfeld equation for plane Poiseuille flow with the Orthogonal Projection method within NDSolve. The Orr-Sommerfeld equation is (a "stiff" problem); $\psi''''(x) ...
1
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1answer
31 views

Error following a variable in an ODE [closed]

I am trying to solve a 4th order differential equation and this is my code thus far ...
0
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0answers
43 views

Resources about Geodynamics

I'm about to start a small project on numerical geodynamic. If possible, I whish to handle the computational work in Mathematica. The project will be small but probably not so small I can do all by ...
0
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0answers
96 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: ...
14
votes
1answer
475 views

Has this implementation of FDM touched the speed limit of Mathematica?

Still, I'll use the implementation of the 1D FDTD method (you can simply understand it as a kind of explicit finite difference scheme for the Maxwell's equation) as the example. Just for completeness, ...
0
votes
1answer
87 views

Attempt to solve for Differential Equation - Acc, Vel, Pos in (x,y,z) [closed]

In the problem I'm working on, there is a tennis ball that is subjected to a headwind, tailwind, and crosswind. I am trying to use NDSolve in order solve for the position functions and to eventually ...
0
votes
1answer
73 views

Formulating a second boundary condition to get an alternative solution to a ODE [closed]

I have the ODE $c'(t) = t^2c^3$ with the initial condition $c(1) = 20$. The differential equation $c'(t) = t^2c^3$ (without boundary conditions) has two branch solutions. I want to formulate a new ...
1
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0answers
83 views

Taking a derivative, then squaring a two dimensional numerical function

Context I am interested in first finding an interpolating function of the solution to the linearly damped wave equation. Here is the solution to the LDWE with smooth square inital function : ...
0
votes
1answer
47 views

Plotting a solution of DSolve

I am trying to plot a solution of a differential equation system. This is what I have: ...
1
vote
1answer
87 views

Mathematica doesn't know the answer to this differential equation system

I am having some trouble with solving a somewhat heavy differential equation system, which is consisted of 10 variables and other abstract parameters as follows: ...
0
votes
0answers
33 views

Finding derivatives in a differential equation system

I have a differential equation system with 10 variables whose functional forms are: $\lambda_R = \alpha_0 + \alpha_1 P_R$ $E_R = \theta_0 + \theta_1 P_R$ $\lambda_X = \beta_0 + \beta_1 P_X$ $L_D = ...
1
vote
1answer
49 views

Code for time derivative or time differential equation

I have three variables $X, Y, Z$ whose functional form is the following (I also have a function for $Z$ which is somewhat complicated but is not essential for my question here; so it is omitted.): ...
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1answer
76 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
2
votes
0answers
78 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
0
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0answers
42 views

NDSolve with mixed boundary conditions

I am trying to solve a spherical Laplace equation subjected to Neumann boundary conditions in the lower half ($θ < π/2$) and constant potential in the other half (say, $f(R,\, θ) = 0,\, {\rm if}\ θ ...
2
votes
1answer
175 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
1
vote
1answer
111 views

Smoothing a single rectangular pulse in NDSolve

Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin. I am looking for a smooth function that looks almost exactly the same as the square wave ...
3
votes
0answers
58 views

Increasing MaxPoints in NDSolve results in memory issue

I am interested in increasing "MaxPoints" in NDSolve's "MethodOfLines" in attempt to increase the resolution of the plot of the solution of linearly damped wave equation with transparent boundary ...
2
votes
0answers
89 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
0
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0answers
57 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
0
votes
1answer
64 views

Substitution of a function in a differential equation

Suppose we have a differential equation as follows: g[t_] := t/2 m[t_] := t/3 A[t_] := {{g[t], 1}, {1, m[t]}} p'[t] == A[t]. p[t], p[0] == {1, 0} ...
3
votes
5answers
214 views

Output is Input for a Differential with Sign?

Here's the problem: For one of my classes, we're supposed to use Mathematica to solve the equation y''=y-b*y' for a variety of b values and specified boundary conditions and plot the outputs. There I ...
5
votes
1answer
106 views

NDSolve and Piecewise functions

I want to clarify upfront, This is not a please help me get the answer to my homework question. I know what I need to do I just do not know how to get mathematica to do it. I am working on an ...
1
vote
0answers
22 views

How to update Plot and some output inside NDSolve callback (StepMonitor)

I have the following problem. I am calling NDSolve to solve a system of first order differential equations (nothing fancy), except that the number of equations measures in thousands and the number ...
2
votes
1answer
57 views

Question about using NDSolve with a matrix equation

I tried to use NDSolve to study a matrix-valued differential backward equation. The following program seems to work: ...
1
vote
1answer
97 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
1
vote
0answers
69 views

NDSolve Wave Equation - Triangular Wave Pulse Inital Condition

I am trying to solve a simple damped wave equation with transparent boundary conditions with triangular shaped piecewise function as my initial condition. I understand that there are issues with this ...
1
vote
1answer
86 views

Can I use the values of interpolating points from NDSolve's output? And How?‎

The output of NDSolve is a (list of)InterpolatingFunction(s). In standard output format the ‎elements of interpolation are not ...
2
votes
2answers
90 views

Can Mathematica solve this equation with NDSolve?

Here is my code: ...
0
votes
0answers
46 views

How to remove error at large time in NDSolve

I am kind of amazed by the fact that Mathematica V9 can't solve a linearly damped wave equation at large time t=200 while Mathematica V8 does without giving me a huge deviation. Intuitively, an ...
2
votes
1answer
78 views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
1
vote
2answers
92 views

How to explain NDSolve that functions must be positive only?

I have a simple system of differential equations to solve but both functions should be positive: x[t] > 0 and y[t] > 0 for all t. I was not able to explain NDSolve this fact so it goes x[t] < 0 ...
2
votes
1answer
117 views

How to solve time dependent Optical Bloch Equations for a three level system?

I am trying to solve the optical block equations for three level system which are time dependent, which i generated using the "Atomic Density Matrix" package. When i use the command to solve this 9 ...
2
votes
2answers
141 views

How to get the series coefficient of a function defined by a differential equation [duplicate]

I need a Taylor series approximation for $x(t)$, which is defined by the following differential equation. $\frac{dx}{dt}=-k_1 x+(1-x)k_2 e^{-k_3 t}$, $x(0)=0$ ...
3
votes
1answer
137 views

How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
2
votes
1answer
133 views

Coupled Nonlinear Differential Equations Problem

I have a big problem solving a set of coupled nonlinear differential equations using NDSolve. Solving the equations by themselves works quite well but if I want ...