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Questions tagged [differential-equations]

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

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63 views

Cross coupling in DirichletCondition not supported — conflict with documentation?

Mathematica 12.0.0.0 happily solves the trivial coupled differential system as follows: ...
36 views

InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
307 views

Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution

I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element. LinearSolve: Linear equation encountered that has no solution. And ...
79 views

Can we construct our own NDSolveStateData?

NDSolve can be broken into three stages: NDSolveProcessEquations processes the equations and sets up an NDSolveStateData ...
124 views

Constant positive and negative Gaussian curvature $K$ meridians as orthogonal trajectories

The plot code below depicts two point through which profiles of constant $K$ are drawn positive and negative. ...
99 views

Reconstructing a function from its gradients

I have a list of the components of the gradients, $\partial f/\partial x_i$, of a function $f(x_1,x_2,\cdots)$. Is there some neat way to reconstruct the function $f$? One approach to doing this ...
73 views

WhenEvent error in NDSolve ODEs

I wish to change the term, T'[t] to 0 when S[t]<=0 when I solve ODEs. I have used WhenEvent in my NDSolve part, but it seems not work. The code is ...
325 views

Solving PDE with unreasonable results

I have a simplified version of my chemical reaction problem. Basically it solves the concentration (ca) and grain (g2) diameter. The ca function is depended on particle diameter R, while g2 function ...
80 views

Solve 1D Wave Equation

I wanna model 1D wave equation and plot it, Here is my try so far, ...
40 views

Manipulating a ParametricFunction to handle units

I have a pretty nice way to handle units on a result from NDSolve, which basically consists of converting all of the units to SI, stripping them, calling NDSolve, and then putting the units back. I'll ...
98 views

Line-Dirichlet Boundary NDSolve

I have defined such a Dirichlet boundary conditions which fixes the nodes in a line, however, the results show that only two nodes are fixed, not the nodes in a line, Code: ...
42 views

DSolve Varying Base on Implementation

I am trying to understand the behavior of a system of equations that is derived from: ...
92 views

Problem in NDSolve (Mathematica 7)

Following a piece of program ...
45 views

Problem with module for solving wave equation

Im really new to mathematica and trying to solve a homogeneous wave equation numericallly. I wrote a module for it and wanted to test it but it only returns my input. ...
59 views

Solve and plot PDE on restricted domain

I want Mathematica to solve (I used a picture since when I use mathjax code the editor here says I might be using wrongly formatted code...) So far, I have ...
43 views

Error in PDE: Length of Derivative operator

I am trying to solve Poisson's equation in a cylinder with Dirichlet boundary conditions for the top, bottom, and sides of the cylinder, but I am getting the following error from NDSolve: ...
105 views

Solving a nonlinear PDE

I'd like to know the asymptotic ($t\to\infty$) behavior of $$\partial_tu = -y\partial_{y}u + x^2 + y x \partial_xu - (1 + \partial_xu)^2$$ with $u(0, x, y) = 0$. ...
36 views

NDSolve error with manipulate for 2 coupled ODEs

While trying to solve a system of coupled ODEs (for EVE[t] and FTZ[t]) with Manipulate, I ...
110 views

PeriodicBoundaryConditions an a square

I hope the answer is simple, but I can't see the solution: I want to solve a PDE for u[x,y] under Periodic boundary conditions on say a square size 10 x 10. I.e. <...
139 views

Wave equation: Understanding PeriodicBoundaryCondition

Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions u[x,t==1 ]==u[x,t==x/2] I tried ...
181 views

Fourier Collocation For Heat Equation [closed]

In fact My problem is this $$\frac{\partial u}{\partial t}+\ sin(y)\frac{\partial u}{\partial x}=\nu(\frac{\partial^2 u}{\partial x^2} +\frac{\partial^2 u}{\partial y^2})$$ But I wanted to test the ...
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Convert Part of an Expression Using ExpToTrig

I'm wondering if there's a nice way to convert only parts of an expression, say exponential functions of varible $\theta$ to trig. The motivation is best descripbed by the following example. ...
129 views

Problems in running the non-linear PDE system

I'm new to the mathematica and just try to solve an seemingly simply non-lineal coupled PDEs. It is about the diffusion-reaction kinetics in a pellet.The code seems workable, but keep running without ...
40 views

How to time shift x-axis in mathematica simulation?

I have a simulation from a system of equations that runs from 0 to 50 Normal = NDSolve[{A /. Parameter, A == .1}, {A[t]}, {t, 0, 50}]; That produces: Now ...
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How to use an interpolating function as an intial condition for a PDE? [closed]

I want to be able to approximate a PDE, but my eigenfunction is an Interpolating function. Is there a way I can use an interpolating function as an initial condition in the PDE. For Example: ...
120 views

Using NDSolve on wave PDE on string, when solution given at 2 different times instead of initial velocity?

This is a PDE taken from a Maple document. Mathematica DSolve currently unable to solve it. I wanted to verify Maple solution using NDSolve. This is string of length 1, fixed on the left, and free ...
109 views

Is it possible to find the Rössler attractor using only a set of Lyapunov exponents?

Is it possible to use a set of Lyapunov exponents to determine the orbits of the Rössler system? If so, could how would I go about plotting them? EG. Known Unknown
161 views

Plot the solution from DSolve

I'm trying to solve a differential equation as in the following code: FullSimplify[DSolve[x'[t] == a + b E^(g t) + (c + d E^(-g t)) x[t], x[t], t]] which ...
63 views

DSolve yields a strange character K

I'm trying to solve a linear differential equation as in the following code: DSolve[x'[t] == a + b E^(g t) + (c + d E^(-g t)) x[t], x[t], t] which yields ...