Questions tagged [differential-equations]

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

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2answers
80 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
32 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 ...
3
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1answer
126 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
39 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 ...
3
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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. ...
3
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1answer
90 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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0answers
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 ...
1
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1answer
86 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
97 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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0answers
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 ...
3
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0answers
107 views

Kolmogorov backward PDE with boundary conditions

I am trying to solve numerically Kolmogorov backward PDE with boundary conditions: ...
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0answers
76 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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0answers
82 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
138 views

Confluent Heun function

Does this function (confluent Heun function) exist in Mathematica? I try to solve the following equation, ...
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0answers
56 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 ...
1
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1answer
48 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-...
3
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3answers
88 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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0answers
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] ...
0
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0answers
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.
2
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1answer
185 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 ...
0
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0answers
24 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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0answers
35 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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0answers
78 views

NDSolve issue, potential singularity or stiff system

I have the following parameters, equations, and NDSolve solution set up as such: ...
3
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1answer
53 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
81 views

Calculate sensitivities of differential algebraic equation [closed]

I would like to calculate sensitivities for a DAE. The DAE can be solved in Mathematica by: ...
2
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1answer
42 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 ...
2
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1answer
190 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 ...
1
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1answer
110 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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0answers
61 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: ...
4
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2answers
132 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: ...
0
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2answers
67 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)+\...
3
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1answer
108 views

Solving a system of coupled ODEs

I am trying to solve these 9 coupled ODEs ...
0
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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
70 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 ...
2
votes
1answer
84 views

Plotting a two parameter function evaluated at a specific point [closed]

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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0answers
76 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. ...
1
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1answer
53 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 ...
6
votes
1answer
112 views

Nonlinear differential equation with unknown parameter and integral form boundary condition

I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are, $$\...
3
votes
1answer
114 views

Why can't MMA solve this system of differential equations?

This system of differential equations can be solved in order to obtain the expression of x[t] y[t] z[t] ...
2
votes
1answer
57 views

Maximizing Output from ParametricNDSolve [closed]

Given a system of differential equations that are dependent on two parameters, such as the system below (the equation below is not that important, I am interested in a general procedure given a ...
1
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0answers
37 views

Unexpected stiff system error [closed]

Let there be the following functions ya[t_, x_] := Cosh[t*x] za[t_, x_] := Sinh[t*x] wa[t_, x_] := x*Sinh[t*x]^2 One can verify that the following PDE's hold <...
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0answers
46 views

Heat transport with Neumann bc in older Mathematica versions [duplicate]

Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions: 1) $T(x,t)=0$ for $t<...
1
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1answer
78 views

“Fewer dependent variables than equations, so the system is overdetermined” without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
6
votes
1answer
137 views

Solving Laplace's equation in 2D using region primitives

Fixed in 12.1 I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both ...
1
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1answer
41 views

NDSolve with Events that reevaluate with different Discrete Variables

I have the following problem: I have a set of ODEs and some discrete variables which I can solve successfully. Now I want mathematica to check at every $0.1 \,t$ time step, wether it would increase ...
0
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0answers
70 views

A system of linear differential equations with variable (time-dependent) coefficients

I have searched almost all similar pages discussing a system of differential equations, but none of them discussed the case of variable coefficients. My problem is a bit more complicated, because ...
1
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0answers
78 views

find ODE solutions and suitable initial conditions to get solution

DSolve[2.56 x''[t] == -0.32 x'[t] - x[t] - 0.05 x[t]^3 + 2.5 Sin[t], x[t], t] I want to find the solution and find two initial conditions such that their ...
-2
votes
2answers
90 views

Manipulate NDsolve 1D-reaction diffusion equation

I want to solve the following 1D-reaction diffusion equation: $$\frac{\partial}{\partial t}u(t,x)=\alpha\,\frac{\partial^{2}}{\partial x^{2}}u(t,x)+a\,u(t,x)$$ $$u(t,0)=0\,\,\,\,\,\text{et}\,\,\,\,\,u(...
0
votes
0answers
67 views

Fit a three-pulse sequence

I am wondering how to properly fit the three-pulse sequence shown below. I have tried a method which is fitting the three pulses with three polynominal functions seperately and then finding the x-...

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