Tagged Questions

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

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0
votes
0answers
14 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
0
votes
0answers
18 views

Nested For loop in Mathemaitca for solving FDM problem

I am solving a FDM problem in Mathematica My equation is d[Rho]/dt + beta*Rho= alpha*q dq/dt + v*dq/dx +alpha*q= beta*rho nx = nt = 5; ...
0
votes
0answers
22 views

How to tell NDSolve to ignore small values in choosing step size

I have a very large system of first order differential equations, which can be written (on paper) as dX/dt=F(X), where X is a vector and F is a vector function. All elements of X are strictly positive ...
0
votes
2answers
51 views

recursive depth of 1024 exceeded [on hold]

Can some tell me what is wrong in the following code. ...
1
vote
1answer
90 views

Solving system of differential equations using loops

I have $F$ system of differential equations. Out of those $F$ equations except for first and last I have general form for the remaining equations (say $ dP_{i}/dt)$. Let $dP_0/dt,dP_F/dt$ denotes the ...
0
votes
0answers
14 views

Does existence and uniqueness of a classical solution impose uniqueness of weak solutions to a pde? [migrated]

I wonder if one knows that there exists a unique classical solution of a pde (for instance: Fokker-Planck equation), is one able to conclude that there isn't any weak solution of the pde, which ...
0
votes
1answer
59 views

NDSolve with a constant

I have a simple differential equation like this s = NDSolve[{y'[x] == A y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] where $A$ is a constant. Mathematica gives ...
2
votes
0answers
50 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...
1
vote
2answers
45 views

Solving a differential equation with NSolve and ploting it WITH the use of Manipulate

I want to solve, let's say, this differential equation: y'[x]=y[x]^n Given any initial condition (wich I might want to manipulate too). I want to plot the graph ...
0
votes
0answers
68 views

how to solve a differential equation [on hold]

I am trying to solve the following differential equation: ...
0
votes
0answers
43 views

How to solve system of non linear Differential Equations with 1 independent variable and 3 dependent variables?

I have been trying to solve this system of differential equations using mathematica. $$F(t) B''(t)+B'(t) F'(t)+B(t) F''(t)=0,\\ F(t) A''(t)+A'(t) F'(t)+A(t) F''(t)=0, \\ B(t) A'(t)+A(t) B'(t)=0$$ Here ...
-3
votes
1answer
61 views

Solving a system of differential algebraic equations [closed]

Sorry, everyone! It is my first time to ask questions online. My specific questions is that: I want to use the NDSolve in the Mathematica to solve my system which is shown below in the equation. and ...
0
votes
0answers
44 views

Ordinary Differential Equation - Initialising conditions [closed]

I have a problem with Mathematica, I am trying to put in an ordinary differential equation into Mathematica with the initial condition that n == n0 at ...
0
votes
0answers
12 views

Why choosing small values of Alpha and Beta gives inefficient Runge Kuttan method [migrated]

I have been trying my hand at a past exam paper and one of the questions is as follows: The second-order Runge-Kutta method to solve the equation $ \frac {dy} {dx} = f(x,y)$, $y(x_0)=y_0$ at the ...
1
vote
2answers
116 views

Solving Differential Algebraic Equations as BVP

I am trying to solve a set of DAEs. \begin{equation} -4 \nu (\lambda(s))^{(-1 - 4 \nu)} \theta'(s) \lambda'(s) + (\lambda(s))^{(-4 \nu)} \theta''(s) = -\alpha_y \cos\theta(s) + \alpha_x ...
0
votes
1answer
61 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. ...
0
votes
0answers
60 views

Need help with this integration [closed]

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
votes
0answers
54 views

Why does my code produce NDSolveValue::ndnum? [closed]

I keep getting the error shown below. It appears to be valid, but I am not sure why my I am getting it. ...
0
votes
1answer
47 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 ...
3
votes
3answers
173 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
votes
2answers
118 views

DSolve returning { } when given my ODE

Why does this code return {}? ...
2
votes
1answer
88 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
vote
0answers
62 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. ...
4
votes
1answer
77 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
170 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: ...
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
85 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
votes
0answers
39 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
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
votes
0answers
45 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
votes
0answers
99 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
482 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
88 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
vote
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
48 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
88 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
51 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
78 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
2
votes
0answers
81 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
0answers
44 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
186 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
115 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
59 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
98 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
59 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
219 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
116 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 ...