Questions tagged [differential-equations]

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

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NSolve third order PDE with boundary conditions

I am trying to solve following PDE involving a third derivative with respect to p: ...
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1answer
22 views

insufficient boundary condition error

I wish to solve the initial value kdv equation with a boundary condition that particles are fixed at the end points. Below is my code. ...
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40 views

Virasoro algebra

My question here is very computational. My problem is in mathematical physics, so I want to ask the community what kind of software they use to do the following computation if there is any? Let $$L_{...
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1answer
157 views

How to plot an implicit solution of a differential equation?

The question is to find and sketch the solution of the following initial value problem: $$(x-y)dx+(3x+y)dy=0$$ and for $x=3$ we have $y=-2$. I was able to find an implicit solution using ...
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1answer
40 views

Using AbsArgPlot on parametricNDSolve output

I have solved following equation using ParametricNDSolve $$ \frac{\mathrm d^2y}{\mathrm dx^2} + \left(a + \frac{2}{\pi} b\ \arctan x\right)y = 0 $$ ...
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ParametricNDSolve not accepting equation [duplicate]

I am trying to solve following differential equation $$\frac{d^2y}{dx^2}+(a+\frac{2}{\pi}b\hspace{3pt}\tan^{-1}x)\hspace{2pt}y=0$$ To solve it in mathematica I wrote the following code ...
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53 views

Solution of a Bessel-like Equation with Boundary Condition at Infinity

I am trying to solve the following differential equation: $$x^{2}P''(x) + 2x P'(x)+[\omega^{2}x^{2}+2]P(x)=0\,,$$ defined for $x>x_{0}>0$ and with the following boundary conditions $$f(x_{0})=...
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59 views

Help speeding up matrix exponent of $ 16 \times 16 $ symbolic matrix

I am trying to run the following script which involves the MatrixExp of t times a 16x16 matrix with one variable, ...
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2answers
424 views

How to apply chain rule to a differential equation

There is a simple differential equation $ y''(x) + (\varepsilon - x^2) y(x) = 0 $. If one uses the new variable $ x^2 = s $, using the chain rule, this differential equation becomes $ 4 s y''(s) + 2 y'...
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18 views

Get the field equations of the G-L energy function [closed]

Im new at mathematica and i need to make a programm to find de field equations of the Ginzburg-Landau Energy.
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45 views

Building `W[f_]:=w[t[f]]` out of solutions `w[t]`and `f[t]`of `NDSolve`

I am solving a system of ODEs with NDSolve to some initial condition and obtain two solutions w[t] and ...
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48 views

How to visualize a vector field on a parametrized surface?

I'm solving a differential equation by NDSolve. After solving the equation, I got the solution for $$. But, now I want to visualise the vector(which makes an angle phi with the normal) on the ...
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1answer
77 views

How to tell mathematica polar coordinates belong to mesh?

Context I want to solve a PDE via FEM on a Disk. If I use a Square I can write ...
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1answer
64 views

How can I speed up NDSolve

I have written a simulation that solve a pde, I used a method I found on this site to speed up the calculation but it is still slow. Is there any way to speed up the prosses? ...
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1answer
42 views

Research Explicit Runge-Kutta method / How to find stability function?

I have this initial conditions ...
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3answers
71 views

Solving ODE System and Estimating Parameters with Experimental Data

I am new to Mathematica. I am trying to find out the best-fit values of the parameters appearing in an ODE system of three equations. The three ODE equations are: ...
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51 views

Simulating a partial differential equation, uniform vegetation and bare soil system (2 species)

I want to simulate a system of two plants ,woody and herbaceous species; with starting condition that half of the grid (square grid) is filled with woody specie, the herbaceous specie exist on the ...
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1answer
54 views

Plot in NDSolveValue

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1answer
40 views

Jacobian and Eigenvalues: is neither a list of replacement rules nor a valid dispatch table, \ and so cannot be used for replacing

I have seen many solutions to this error for finding jacobian and eigenvalues and tried but they are not working for me. Here is the code: ...
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1answer
71 views

Homogeneous linear ODEs with time-dependent coefficient matrix, optimalisation of NDSolve algorithm

I would like to ask for advice on the following (probably not too complicated) problem: I have a linear system of ODEs of the following form: $$ \dot{X}(t) = M(t)X(t) $$ where $ X(t) $ is a vector, ...
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1answer
121 views

archimedian spiral from curvature

I am trying to reconstruct an archimedean spiral from its curvature $$\kappa (\text{s$\_$})\text{:=}\frac{s^2+2}{\left(s^2+1\right)^{3/2}};$$ eqns: $$\left( \begin{array}{c} t'(s)=\frac{\left(s^2+...
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Coupled differential equation with variable coefficients

Need suggestion to implement and solve this coupled differential equation in mathematica. $\frac{\delta}{\delta t} F_{1}(x,t)=C_1(x,t)F_{1}(x,t)+C_2(x,t)F_{2}(x,t)$ $\frac{\delta}{\delta t} F_{2}(x,...
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Numerical solution of two cupled ODE [duplicate]

I have two coupled differential equations $$\frac{d^2u(x)}{dx^2}=h\;\frac{d^3w(x)}{dx^3}+K\;u(x)$$ $$-EI\;\frac{d^4w(x)}{dx^4}+A\;\frac{d^3u(x)}{dx^3}+q(x)=0$$ and the following boundary conditions: <...
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Errors in NDSolve for complex matrices

This is the problem. It is quite simple, and looks unwieldy only because I had to rewrite quaternions as complex matrices. ...
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2answers
267 views

Drawing Lines on Differential Equation Slope Field [closed]

I am supposed to create a detailed slope-field for x' = x + t/2 I have made a slope field using: ...
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1answer
96 views

Numeric Solution for 1-D ODE with only Neumann conditions

I tried to solve a simple ODE with only Neumann conditions like But obviously this doesn't work. I must add a useless DirichletCondition to make it work I have verified that the solution is correct, ...
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1answer
46 views

How to find the power series solution of this ordinary differential equation using MMA

I already know that the solution of this differential equation $y''(x) - x*y(x) = 0$ can be expressed by the following power series: $$y(x)=c0(1+\frac{x^{3}}{2\times3}+\frac{x^{6}}{2\times3\times5\...
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1answer
71 views

How to solve the differential equation of a Brachistochrone Problem

This is a differential equation to solve the most brachistochrone line, but it can't find the exact analytical solution : ...
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44 views

1D time-dependent Schrödinger equation with absorbing boundary

I'm trying to solve the 1D Schrödinger equation subjected to an absorbing condition using NDSolve but cannot seem to set up the absorbing condition... My problem ...
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35 views

Coupled ODEs: step size is effectively zero; singularity or stiff system suspected

I have seen many solutions to this error and tried but they are not working for me. Here is the code: ...
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77 views

Solving equations using Implicit-Runge-Kutta method

I am trying to solve the system of equations using Implicit-Runge-Kutta method but mathematica is showing error "NDSolve::ndcf: Repeated convergence test failure at [Tau] == 4.9`; unable to continue."....
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52 views

Small issue with PDE initial condition

I'm trying to solve the Fokker-Planck equation $$\frac{\partial p}{\partial L}(L, \eta)= \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial \eta}(L, \eta)\right] = ...
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How to solve this system of coupled differential equations (numerically) [duplicate]

I am trying to solve this system of coupled differential equations, code: enter link description here The problem is when I run the code, it appears: NDSolve::ndode: The equations {True} are not ...
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68 views

How to solve numerically this system of coupled differential equations

I am trying to solve this system of coupled differential equations, ...
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1answer
123 views

Help with implemented Piecewise in Module

Suppose we have an ODE in the form: f''[r] + f'[r] == t f[r]+h[r] where ...
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1answer
154 views

How to plot trajectories of the Rossler System [duplicate]

This is my current homework problem. I have completed parts a and b, but am now stuck on part c. I'm not sure what it means by plot the trajectories with different initial conditions, nor am I 100% ...
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1answer
114 views

Why can't I solve a system of four third-order partial differential equations using NDSolve?

I solve the problem of optimal control. First, I solve a system of two equations (with respect to the variables p, q, V, n) with already optimal conditions (Kopt and Sopt) to check whether it is ...
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I want to plot root of the following complex equation

I am trying to plot the roots of the following equation as mentioned in the code below But it is not giving me output. If anyone can resolve this problem for me is most welcome. ...
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1answer
90 views

Using Around with NDSolve

I was trying to obtain the same result of a differential equation with to different methods the first one is based on DSolve and the second one is based on NDSolve ...
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1answer
42 views
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1answer
65 views

Cryptic NDSolve::nlnum when working with matrices

This problem was initially formulated in quaternions, but I had to rewrite them to complex matrices (as they seem to be supported better). Possibly introducing some errors along the way. So the ...
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2answers
88 views

RK4 residual error for ODE

Below I am giving the code that I am using ...
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1answer
82 views

System of pde with Neumann boundary conditions

The Ginzburg-Landau equation for a system of squared superconductor with a slit in presence of a uniform magnetic field can be written as a sort of continuity equation with Neumann boundary conditions ...
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1answer
48 views

how to solve a Partial Differential equations numerically of the kind given below [closed]

eq=D[f[x,y],y]+ f[x,y]/y == Q[x,y] The equation doesn't have any derivative with respect to x. If I use the following syntax for ...
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0answers
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NDSolve and quaternions

I have tried to solve a set of equations of motion in Mathematica and got an error. Then, I simplified it as much as possible, and the following example gives the same error. ...
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Log plot of residual error for numerical solution of ODE

Below I am giving the code that I am using ...
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1answer
157 views

Solve an ODE with parameters in a boundary condition

Consider the ODE: ode = y''''[x] - 2*k^2*y''[x] + k^4*y[x] == I*k*a*((2*x - x^2 - c)*(y''[x] - k^2*y[x]) + 2*y[x]); in which a...
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120 views

Coupled PDE equation or boundary condition creating singularity issue

Previous post: Using NDSolve and PieceWise for boundary conditions for coupled PDEs I realised that my previous post was a little vague so I hope this post clarifies any confusion. I've looked over ...

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