Questions tagged [differential-equations]

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

4,213 questions
61 views

Solve a Differential equation analytically instead of numerically

I want to solve the differential equations (shown below in the list 'eqs') analytically instead of numerical. Using NDSolve the following code works perfectly fine but using DSolve it doensn't. I ...
107 views

Vector ParametricNDSolve and FindRoot interaction

This question came out of this question. I have a set of differential equations, written in vector form. I'm only interested in the value of these at the endpoint, and so I use ...
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Why DSolve gives the error “Arguments should be ordered consistently” on this PDE?

This problem is strange. Mathematica is able to solve this PDE with no error ...
2k views

Turing patterns

I am new in learning Turing patterns. Is there any sample code available to generate such patterns in ecology model (Lotka–Volterra model)? The above figure is taken from this paper, and is based on ...
483 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
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Using ParametricNDSolve to solve a hysteretic ODE (Wolfram Mathematica 10.0)

I am trying to solve an ordinary differential equation using ParametricNDSolve and I want to fit the solution to some data to get the value of the parameter. The problem I have is that the ODE is ...
115 views

Mathematica unable to interpret equations in DSolve

I'm trying to solve a system of seven ODEs with seven conditions. Since the following approach using DSolve is yielding the same output as the input, Mathematica can't find a solution. ...
85 views

Vector-valued ParametricNDSolve, solving for a combination

I am integrating two vector differential equations using ParametricNDSolve, one for $\mathbf{Y}$ and one for $\mathbf{Z}$, and then I'm interested in a combination ...
64 views

Hat function(UnitTriangle[x]) is really applicable in Finite Element Method?

I am learning finite element method(galerkin method) for solving ode/pde. when searching this topic, I often see examples using the hat functionUnitTriangle[x] as ...
56 views

Formulating equations for 3D stress in the finite element method

I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
156 views

Solving linear coupled PDEs by FDM

I am trying to solve some linear, coupled PDEs for perturbative analysis (first order in time, 3rd order in space), for which I then plan to take the global spatial maxima of their magnitudes and plot ...
74 views

NDSolve cannot evolve Gaussian wave packet with small width

I want to solve a 1d wave equation with initial conditions: $$u(x,0) = f(x) = e^{-(x - x0)^2/2\sigma^2} \ \ \text{and}\\ u_t(x,0) = - f_x(x)$$ The second condition is the advection equation and ...
53 views

WhenEvent ignores some actions

I've got a problem where WhenEvent successfully detects an event, but then performs only some of the actions. In this minimal example, ...
51 views

Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
81 views

How to put solutions of mutiple DEs with NDSolve in table

I have $N$ differential equation for each $s \in {1,2,...,N}$ on the domain $x \in [1,2]$ of the form (e.g.) $xf_s'(x) + \log(xs) f_s(x)+1 = 0$, with the boundary condition $f_s(1) = e^{-s}$ Now I ...
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Mathematica running out of RAM while executing NDSolve

I am playing with Mathematica to solve the 2D-wave equation with the code below: ...
437 views

Plot exactly N bounce of a ball

I want to plot exactly N bounce of a ball. I'm using DSolve to solve the differential equation and WhenEvent to change the velocity. The code below plots only the first 10 seconds. ...
39 views

NDSolve: evolutionary singularity in coupled differential equations

I am trying to solve coupled differential equation where a function attains a value such that its derivative is infinite. ...
660 views

How to plot an unstable attractor?

I'm trying to solve and plot the following in Mathematica: ...
282 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
175 views

Fitting multiple data with model and NDSolve with different initial conditions, and other shared parameters

I know that there are already questions about fitting multiple datasets and about NDSolve and about shared and non shared parameters, but I tried to apply them and some things are still not clear. ...
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Fitting system of differential rate equations to data

I am trying to fit a set of differential equations to experimental data, without luck so far. These are the data: ...
42 views

Evaluation Control for Equation Input to NDSolve

I am trying to numerically integrate a system of equations using NDSolve and am having issues with symbolic matrix inversion taking a long time. The actual system is much more complicated, but I have ...
35 views

Calculation of evolution equation with NDSolve

I have near to no experience with mathematica, so this might seem pretty trivial. I want to solve an Evolution equation, i.e. we have a function $f(t,x)$ and a differential operator $T(t,\partial_t)$. ...
41 views

ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
45 views

NDSove vs ParametricNDSolve

ParametricNDSolve is very practical when one has to execute NDSolve again and again. However is it equally accurate? I have not ...
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WhenEvent versus If function for ODEs

The following equation works for ParametricNDSolve ...