Questions tagged [differential-equations]

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

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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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55 views

Solving two ODEs together

Why does Mathematica not give any output when I am trying to use DSolve to solve these two equations? ...
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37 views

system of pdes equations

Is it possible to solve those group analytically in Mathematica? ...
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29 views

NDSolve pde with boundary conditions more than equation required

I have a pde which is first order in time and second-order in space. I have a boundary condition in time and two boundary conditions in space at the outer edge; this results in a smooth solution. ...
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155 views

Why does DSolve fail in this first order differential equation?

I am trying to solve the following first order differential equation: $$ g'(R)=-2 \sqrt{R^2-g(R)}+2 R$$ By direct substitution it can be verified that an obvious solution is $$g(R)=R^2$$ ...
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1answer
40 views

Problem with DSolve, NDSolve with WhenEvent, Boundary Value Problem

I got the same problem as in question: DSolve, NDSolve with WhenEvent Give Incorrect ...
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1answer
54 views

Solving system of partial differential equations

I am solving two PDEs together for two functions y, G: ...
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38 views

Nesting differential operators

Suppose I define differential operators $d=x\frac{\partial}{\partial x}$ and $L=g(x)d^4$ (so that $L(f)=g(x)(x\frac{\partial}{\partial x})^4f$ ) and I want to expand the differential operator $L=a_0+...
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1answer
66 views

Differential equation with interpolation

If I have a second-order nonlinear differential equation as follow: sol = NDSolve[{*w''[z] - G[z]*w[z] == 0, w'[0] == 100, w[L] == 0.001}, w[z], z] where: <...
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1answer
44 views

Hyperbolic Second Order PDE - boundary condition with sinusoid

This is similar to countless PDE equations, but the error seems specific to my case: I'm trying to solve a hyperbolic PDE, where $U=(x,t)$ and $V=(x,t)$: The system represents a piezoelectric beam ...
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1answer
129 views

Updating a graph under ODE dynamics (vertex model)

Consider the following graph, which is obtained from a VoronoiMesh ...
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3answers
585 views

Finding orbits in the Schwarzschild spacetime

I am trying to plot Schwarzschild's orbit without invoking the geodesic equation. As a reference I am using Chandrasekhar's Book (The Mathematical structure of Black Hole, OUP). In page 98 of the ...
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2answers
79 views

Manual ArcLength sampling on spline differs from MeshFunction sampling

Using Michael E2's answer, I performed a manual arclength parameterisation by solving the differential equation (or: finding the inverse of a function whose derivative is known). I compared the ...
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1answer
30 views

How to use conditional clause inside NDSolve

I am trying to solve a differential equation that changes its behaviour depending on the value of the dependent variable. I've tried as shown below, but the computer does not understand my If clause ...
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1answer
121 views

Solution of coupled differential equations

i was wondering if somebody could help me solving the following two coupled differential equations... $$\Delta u_{xx}(x)=dw_{xxx}(x)+\frac{K}{EA}\Delta u(x) \\$$ $$-EI_\infty w_{xxxx}(x)+2d\,EA\;\...
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1answer
38 views

How to plot parametric time dependent plot with different parameters taking average of time?

I am trying to plot the solution given in the code with respect to "delc". Now the problem is that it can be plot for a particular value of "t" like t=10,20,50,60,.. upto 100 but what i need is mean ...
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3answers
313 views

How to solve n sets of coupled equations in mathematica?

I have a lattice (1D) problem to solve, where I have $n$ particles, and each are coupled to neighbours via a harmonic potential. ...
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1answer
87 views

Display returned integral containing assumptions with integral sign

From solving the PDE example of the general 1 dim heat equation in Nasser Abbasi's site https://www.12000.org/my_notes/pde_in_CAS/maple_2019_and_mma_12/insu157.htm#x182-1810003.1.1 (his problem No 151)...
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41 views

Kernel shutting down with no error message in Linux while it does not happen in Windows

When I run the code to solve ordinary differential equations using NDSolve, the code is stopped with no error message in Linux while it does not happen in Window. Specifically, the code solves the ...
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1answer
77 views

Solving Poisson equation with Robin boundary condition with DSolve

I have the following BVP: $-\Delta u = f \;\;\;\text{in}\;\Omega=(0,1)^{2}$ $u+\varepsilon\nabla u\cdot n = 0, \;\;\;\text{on}\;\partial\Omega$ where $f(x,y) = 2x(1-x) + 2y(1-y)$ and $\varepsilon>...
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1answer
73 views

Solve age-structured SIR model (i.e. a PDE) in Mathematica

I am trying to solve an age-structured model of disease transmission, where people fall into four compartments: susceptible to both strains, $x(a,t)$; those who have been exposed to strain 1, $z_1(a,t)...
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46 views

How to set correct initial conditions while solving a Differential Equations set?

I tried to solve a physical problem (IYPT No.7 Balls on a String) by referring to the example/DoublePendulum in the help document. However, an error was reported when the program running. Where are ...
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99 views

Kolmogorov backward PDE with boundary conditions

I am trying to solve numerically Kolmogorov backward PDE with boundary conditions: ...
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61 views

Differential Transform Method

I Want to solve the following differential equation by differential transform method D[u [x], x, x] + B*D[u [x], x]^2 + A*u[x] == 0; with the boundary condition ...
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81 views

Using NDSolve and PieceWise for boundary conditions for coupled PDEs

I've decided to try and use PieceWise in my boundary conditions for my 4 coupled PDEs, but it doesn't seem to work out nicely. I'm receiving the error: NDSolve::overdet: There are fewer dependent ...
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1answer
110 views

Confluent Heun function

Does this function (confluent Heun function) exist in Mathematica? I try to solve the following equation, ...
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55 views

Hopf bifurcation for competitive system

I am attempting to visually investigate a Hopf bifurcation in the xz plane in a competitive system but have no idea how to input some of these values so I may adjust some of the parameters as ...
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1answer
45 views

Can this PDE be solved through DSolve?

I was trying to solve the linear advection pde, using DSolve. I was able to do it using NDSolve, but I was curious to see if Mathematica was able to give the well-...
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3answers
80 views

Plot an Integral of NDSolve solution

I have a problem with plotting the integral of an NDSolve solution. I have attached the code for a simple 2nd order linear ODE to be solved by NDSolve and then to be integrated by NIntegrate. I ...
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46 views

I there any way to DSolve an equation by an estimated method?

I am trying to DSolve this differential equation for A[r] ...
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55 views

Calculating with deformed Heat equation?

How can I implement the following equation and start computing numerically? The first partial derivative can take fractional numbers.
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1answer
184 views

Need help solving ODE with ParametricNDSolveValue solver

I am trying to apply @bbgodfrey method for finding the right initial guess for the following problem but I get an error message and I don't understand where it comes from. I would also like to ...
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23 views

Clear assigned y'[x] from memory [duplicate]

If I, by mistake, write Mathematica assigns $y'(x)=y(x)/5$ and I don't know how to clear that from memory (I had to restart Mathematica). ...
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33 views

Optimal way to approximate initial condition for PDE?

I have a Fokker-Planck PDE \begin{align} \frac{\partial p}{\partial L}(L,\eta) = \eta^2\frac{\partial^2 p}{\partial\eta^2}(L,\eta) +(1-2\eta)\frac{\partial p}{\partial\eta}(L,\eta)+\frac{2(\eta-1)}{\...
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78 views

NDSolve issue, potential singularity or stiff system

I have the following parameters, equations, and NDSolve solution set up as such: ...
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1answer
50 views

Numerical Issues Using Results of NDSolveValue

I am solving Laplace's Eqn. (Cartesians) in 2D in a region which is infinite in x, semi-infinite in y, and bounded by a function of x (h[x] in my code) close to y=0....
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1answer
108 views

How to plot solution of first order time dependent differential equations with other parameter not with time

I am trying to plot the solution given in the code with respect to "delc", not w.r.t time "t". I don't know what to do for getting the plot between solution and value "delc" which vary 0 to 2. The ...
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1answer
79 views

Calculate sensitivities of differential algebraic equation

I would like to calculate sensitivities for a DAE. The DAE can be solved in Mathematica by: ...
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1answer
39 views

AppendTo inside ParallelMap

I think this question has never been fully answered. In here the problem has already been mentioned, but let me give a MWE. I will solve a given ODE for a wide range of initial conditions and I want ...
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1answer
186 views

The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions

The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions ...
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1answer
104 views

A system of differential equations [closed]

Consider the following system of differential equations: $$x'(t) = a\, x(t) - b \,x(t) y(t),$$ and $$ y'(t) = c\, x(t) y(t) - d \,y(t),$$ with $$ x(0) = x_0, y(0) = y_0$$ For example, we may have: <...
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59 views

Ground state Of Gross Pitaevskii Equation

I want to plot the ground state of Gross-Pitaevskii equation using NDSolve. I am using the following code: ...
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2answers
111 views

NDSolve and Euler method

I would like to solve $y'(x)=x^2-y^2,y(0)=4$ with two ways, NDSolve and Euler method, and with Runge-Kutta maybe. Then, I 'll try to plot all of them in one graph. I had with NDSolve: ...
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2answers
65 views

Shooting with updating BC's

So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
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1answer
100 views

Solving a system of coupled ODEs

I am trying to solve these 9 coupled ODEs ...
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0answers
30 views

NDSolve error when integrating two second order coupled ODEs

I want to plot a solution for a system of two second order coupled ODEs: ...
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1answer
66 views

Adjusting PrecisionGoal and AccuracyGoal when solving my equation using NDSolve?

Thanks for paying attention to my question and modifying my terrible formatting[facepalm], now I think I've found the answer. The point is the selection ...
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1answer
78 views

Plotting a two parameter function evaluated at a specific point

I am trying to solve the following problem: given the differential equation $$\frac{d^2y}{dx^2}+\bigg(a+b\frac{2}{\pi}\tan^{-1}x\bigg)y=0$$ subjected to two different initial condition we get two ...
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65 views

DSolve function is not working for Hypergeometric Function

I am trying to get the solution of second order differential equation, but it is not working. Any idea about it will help me a lot. ...
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1answer
50 views

Error message when trying to solve 2 coupled PDEs using NDSolve

I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages: NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...

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