Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
7,578
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Solving lengthy higher order pde using finite difference
I am attempting to solve a very massive pde (latex expression given below).
I have done some work with finite difference before for relatively simple equations (like heat diffusion or the wave ...
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Solving a system of differential equations connected by boundary conditions [closed]
I'm trying to numerically solve a system of second order differentials equations that are connected only by boundary conditions. I can't figure out how to define the problem in mathematica.
The first ...
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"Singularity or stiff system suspected" and "Input value lies outside of range" errors when plotting complex pendulum
This is my first time posting a question so apologies for any issues.
I'm a first year physics student who just started using mathematica last week. Part of my physics course is to create a computer ...
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296
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differential equation precision issue
I am attempting to get a shooting method set up, but I am having some trouble finding a solution. I originally had the below code
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How to Consider knowledge about solutions interval in ndsolve
I want to find b[x] and c[x] in the interval 0<x<1. Equations to be solved are 4 coupled equations as below
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system of coupled equations
I want to solve system of coupled equations for b[x,t] and c[x,t]:
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134
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How to define inclusions in FEM/NDSolve? [closed]
I am trying to simulate the compaction process of hot mix asphalts and want to do this with mathematica's FEM libraries. How can I define inclusions in meshes (i.e aggregate particles in the binder) ...
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111
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NDSolve: Improperly assigned stepsize
This is not a question which I estimate is aided in answering by providing complete code, which is excessively long.
I ran an NDSolve[] at ...
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334
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Improve speed of RK4 algorithm for solving ODE
For anyone with interests in dynamical system, i'm trying to plot the phase space of a given hamiltonian.
My code is this:
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643
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Different results from ode45 and NDSolve?
I am solving nonlinear ODE + integration groups using NDSolve of mma and ode45 of matlab. At last, I found that they give different results, even after I added RungeKutta method, interpolationorder, ...
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Differential algebra package in Mathematica
Is there any equivalent of Maple's differential algebra package in Mathematica?
In particular, the Rosenfeld-Groebner algorithm has been implemented?
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DSolve non linear DE [closed]
probably my problem i´m gonna ask seems ridiculous and quite basic.
I want to solve an equation with the following code, where a,b,c are parameters. But surprisingly they don´t appear in the solution. ...
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Any possible to save a 'partial' result of NDSolve when it was aborted due to insufficient memory?
I have run a NDSolve code for an extremely long time. Unfortunately, it was aborted because there was insufficient memory available to complete the computation. At ...
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Fitting Three-Dimensional Data with Parameters
I have been trying to fit a model of rate equations to data of three dimensions. The rate equations in my model are as follows.
...
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Looking under the hood of DSolve [closed]
Is it possible to print out information about the algorithms DSolve uses to solve a differential equation?
I'm looking for something similiar to this Maple procedure. It lets you specify how much ...
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Behavior of solution to a ODE near a singular point [closed]
I want to see how the solution to the following ODE looks near z=z0.
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Vinculated boundary conditions [closed]
I have a problem in the form:
$-y''(x)+V(x)y(x)=0 $
with the initial conditions:
$\quad y'(0)=k \ y(0), \quad k=cte$
The $V(x)$ is a model's parameter, for example $V(x)=\frac{6}{\left(x+2\right)^...
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Problem with ParametricNDSolve and FindMaximum [closed]
I have a system 4 coupled differential equations:
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Solving 4 coupled differential equation and minimizing the solution
I have a system of $4$ coupled differential equations.
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Setting different B.C. for different fields in NDSolve
My question regards construction of a PDE solver for several fields, with different type of boundary conditions for several fields.
Say I have the following set of equations:
$$ \partial_{t}\rho+v\...
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PDE: Specify AccuracyGoal, StepSize, and WorkingPrecision interval-wise [closed]
I am using Mathematica 8.
I have two ODEs (in time) and a diffusion PDE (in radius and time) which are all coupled to each other. I solve them using NDSolve by ...
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Differential equation: NDSolve::berr
I'm trying to solve the following differential equation. I'm able to obtain a solution, and that solution looks more or less as how the theory predict it should be.
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714
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Wave equation PDE with changing boundary condition [closed]
This is my first post here, normally with mathematica I will solve out the PDE using eigen function expansion or separation of variables and then model the solution in mathematica. However this time I ...
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Solution of the Lagrange's minimal surface equation [closed]
Can I use Mathematica to solve the Lagrange's partial differential equation?
$$(1+f_y^2)f_{xx}-2f_xf_yf_{xy}+(1+f_x^2)f_{yy}=0$$
I tried:
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Solving ode which solution oscillate violently
This is a ordinary differential equation:
y[x]/(-1 + x^4)^2 - ((1 + 2 x^2 + 3 x^4 - 2 x^6) Derivative[1][y][x])/(x - x^5) + Derivative[2][y][x] == 0
I want to ...
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How to "INJECT" with holding Evaluation, specifically into a WhenEvent
I am importing a set of differential and stochastic equations from an external package, and want to use Mathematica to analyse this.
I am struggling building the set of equations that I can use with <...
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DSolve does not give an analytic solution for a tutorial input [closed]
I am just starting with Mathematica and I have tried to solve PDE following DSolve, with first three inputs from the Elliptical Partial Differential equations ...
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385
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NDSolve for an (slightly) discontinuous Piecewise input
I define a Piecewise discontinuous function V[f[t]], which depends on a function f[t] I want to get numerically using ...
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Solving two PDEs (for f[x,y] and g[x,y]) coupled through a non-linear function |Grad[f[x,y]]|^2
I am new to Mathematica, trying to solve two PDEs (for f[x,y] and g[x,y]) coupled through Grad[f[x,y]]. In the following code when n is set to 1, NDSolve seems to be able to solve for f[x,y] and g[x,y]...
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453
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How to use interpolating functions in NSolve with a piecewise function?
I have a system of two non-linear differential equations that are piecewise, the solutions of which I would like to use to obtain the values of a third variable that is also piecewise. I have trouble ...
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NDSolve with (approximately continuous) Piecewise input
I am finding some troubles when using NDSolve with this piece of code:
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648
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Getting FindRoot::nlnum when trying to find root of an Interpolating function [closed]
I want to solve a system of differential equations and find a point where the solutions cross. So four steps:
1. Solve the system of differential equations:
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How to find the eigenvalues of a custom operator using NDEigensystem? [closed]
I would like to solve a Hamiltonian presented by a 2x2 matrix. Hamiltonian is given by:
...
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DSolve throws an error about Solve and returns unevaluated [duplicate]
I evaluate:
DSolve[{2*y[x] + y'[x]^2 + a*x^b == 0}, y[x], x]
During evaluation of In[26]:= Solve::ifun: Inverse functions are being used by Solve, so some ...
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NIntegration and DSolve with same variable
I need to solve this problem:
Then follows the code, with:
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Fourier-style solutions to differential equations, not piecewise polynomials
NDSolve returns piecewise polynomials. Is there any way I can get a
single (non piecewise) function consisting of sines and cosines
instead? Sort of a "Fourier approximation" to the solution of my
...
user1722
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Solving a simple ODE [duplicate]
I am trying to solve $y(x)' = \sqrt{y(x)}$ with initial condition $y(0)=0$ for $x\in \mathbb{R}$. I have tried this:
DSolve[{y'[x] == Sqrt[y[x]], y[0] == 0}, y[x], x]
but this gives
{{y[x] -> x^2/4}...
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NDSolve memory usage [closed]
I am trying to solve numerically a system of linear ODEs with some quickly varying driving functions. The basic command is:
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Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]
I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
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DSolve doesn't give an output for a system of ODEs
I'm trying to solve a system of four ODEs. However, DSolve doesn't give any output (no mistake either).
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Help with calculating a complicated integral
Edit: The question is solved : )) Thank you for your attention !
I am sorry for mass questions, but the question bothers me a lot. So I would like to ask this question here.
This problem arises when ...
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How to make a parameter stochastic in a differential equation system with NDSolve?
I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
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PrecisionGoal and AccuracyGoal making the solution less accurate?
I am having this differential equation:
...
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Eliminate a variable from a differential equation and an algebra equation then collect the remaining variables
Recently, I am attempting to eliminate a variable from a differential equation (DE) and an algebra equation (AE), then collect the remaining variables as a new (grand) parameter. Actually, I have ...
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How to understand the symbolic integral in a result returned by DSolve?
I am trying to solve an ODE like
$$\frac{dF}{dx}=\frac{a}{\ln^3 x+[c+d(ax+b)][2\ln x+c+d(ax+b)]\ln x},$$
where $a,b,c,d$ are constants. I guess it could contain a special function, say, the ...
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Easy way to get the boundary of a geometric object [closed]
I am trying to define von Neumann boundary conditions for a prism. To do so I need the boundary of the geometric object. I can't seem to find an easy way to do this. I have tried to hard code a ...
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Cylindrical Coordinates with NDSolveValue [closed]
Can anyone help me figure out how to set up a solution for NDSolveValue that incorporates the use of Cylindrical Coordinates. I tried using SetCoordinates[Cylindrical] but it is not working (as in it ...
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Combining Manipulate and NDEigenvalues [closed]
I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following
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Time evolution of a bispinor [duplicate]
The effective Hamiltonian for polariton graphene is given by:
...
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Getting ALL solutions of the logistic ODE with DSolve?
In Mathematica 10.0, the command
DSolve[y'[x] == y[x]*(1 - y[x]), y[x], x]
gives
{{y[x] -> E^x/(E^x + E^C[1])}}
I take ...
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