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

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9
votes
2answers
2k views

How to discretize a nonlinear PDE fast?

I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
0
votes
1answer
70 views

NDSolveValue with a multiple variable equation

I'm trying to plot this equation of motion for a pendulum with a periodically applied torque for 20 cycles, where b, m, L, g are given constant values. ...
3
votes
3answers
195 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. ...
10
votes
2answers
527 views

DSolve cannot solve for certain branches of the solution

Update - This has been fixed in 10.0.0 Could somebody please tell me, why I am always getting an error message when trying to run the following code: ...
15
votes
4answers
524 views

Accessing Reduce from DSolve

When solving transcendental equations, Solve frequently warns us that inverse functions are being used so that some solutions may not be found. We also see that ...
0
votes
1answer
67 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 ...
2
votes
2answers
119 views
5
votes
2answers
200 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: ...
4
votes
1answer
104 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 ...
1
vote
0answers
69 views

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

I am trying to solve two differential equations representing the position of an object in space. I have specified arbitrary initial conditions. ...
2
votes
1answer
154 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 ...
2
votes
3answers
356 views

Constraining function found by NDSolve to stay positive

I am trying to constrain my variables in NDSolve so that they stay positive for the integration interval. Is is possible to do that? Using Assumptions as in ...
1
vote
2answers
101 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 ...
14
votes
1answer
524 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, ...
2
votes
1answer
83 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
5
votes
1answer
101 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 ...
12
votes
1answer
790 views

I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve

The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is: ...
2
votes
1answer
223 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 ...
0
votes
0answers
46 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
vote
1answer
32 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
votes
0answers
152 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: ...
0
votes
0answers
47 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 ...
2
votes
0answers
89 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
votes
1answer
98 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
76 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 ...
3
votes
5answers
236 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 ...
1
vote
0answers
87 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
571 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
1
vote
1answer
96 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
1answer
53 views

Plotting a solution of DSolve

I am trying to plot a solution of a differential equation system. This is what I have: ...
0
votes
0answers
34 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
56 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.): ...
1
vote
1answer
111 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
1answer
204 views

Indexing of Large Autonomous System of Equations for Use in NDSolve

I currently have a list of ~150 autonomous ODE's that I need to be able to work with using NDSolve. Fortunately I already have them formatted in plaintext, which ...
0
votes
1answer
84 views

Getting message DSolve::conarg:

I want to solve a simple linear PDE about $p_0$ which is a function of ξ, ζ and τ. However, the boundary condition is defined at ζ = h, which is a function of ξ and ...
0
votes
0answers
59 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 ...
1
vote
1answer
142 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
64 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 ...
0
votes
1answer
124 views

Specifying initial conditions for a PDE

I have simple diffusion equation with point source at c(0, t) = 1 and initial condition c(elsewhere, 0) = 0. How should I apply ...
2
votes
0answers
166 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
votes
0answers
65 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
0
votes
1answer
67 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} ...
5
votes
1answer
156 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
1answer
120 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 ...
1
vote
0answers
33 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 ...
1
vote
1answer
126 views

NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
2
votes
1answer
66 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
0answers
93 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 ...
0
votes
0answers
48 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 ...