Questions tagged [differential-equations]

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

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1answer
70 views

Numerical solution to Differential equation

I want to get the differential solution numerically. I used wolfram alpha. here is the link. I tried this code on the Mathematica file. ...
5
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1answer
75 views

How Does StreamPlot Handle Singularity or Indeterminates?

I will like to know how StreamPlot finds its way around singular/indeterminate values. Actually, I was thinking of using ...
5
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1answer
94 views

Why DSolve gives different answer depending on order of variables: $u(x,t)$ vs. $u(t,x)$?

Using V12 on windows 10. I would think it should not matter if one uses $u(x,t)$ or $u(t,x)$ in the specification of the PDE, as long as everything else is consistent (keeping the initial condition ...
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3answers
224 views

Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
6
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1answer
219 views

Controlling dynamic time step size in NDSolveValue

Statement of problem I'm writing a script to calculate the temperature of a 2D system with time-dependent heat deposition. The heat deposition is a square wave pulse of duration w = 10^-6 seconds, ...
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0answers
59 views

Implicit function definition and variable change

in my code I solve a non-linear system of ODE to obtain the positive functions RadEnDens and PhiEnDens, everything as a function ...
16
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1answer
1k views

How to solve the tsunami model and animate the shallow water wave?

Backslide introduced in 9.0, persisting through 11.3. Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation. How to ...
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1answer
71 views

DSolve returns unevaluated(I need a closed or numerical solution for this system and plot solution)

I am trying to find a solution to this system of differential equations but the program gives the same output without any messages. I would like help. Please find the Mathematica code posted here. a ...
5
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1answer
194 views

Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
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0answers
94 views

Why doesn't NDEigenSystem give smooth eigenfunctions? [closed]

I'm looking for smooth solutions of the 1D Helmholtz equation $\left[\frac{d^{2}}{dx^{2}}+k_{0}^{2}\epsilon(x)\right]\phi=0$ with homogeneous Dirichlet boundary conditions, where the permittivity $\...
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2answers
79 views

MoL: How to enforce Chebyshev–Gauss–Lobatto points in SpatialDiscretization?

In Mathematica documentation one is prompted to use a grid with points at the zeros of the Chebyshev polynomials so that Runge's phenomena arising from ...
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0answers
61 views

Next maximum plot with results from NDSolve

I want to produce a Next-maximum-plot, i.e., I want to plot all local maxima $m_{i+1}$ against the local maximum $m_i$ in order to check for chaotic behavior. In particular, I have the following code:...
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1answer
38 views

Coefficient Array from total derivative of expression

I have an expression $$\dot{r}\dot{\eta}+r^{2}\dot{\theta}\dot{\xi}=0$$ where $\eta$ and $\xi$ are both functions of $r,\theta$. In MM I wrote this as ...
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1answer
63 views

Unexpected error when implementing FEM in MoL SpatialDiscretization

I cannot figure out why the following piece of code ...
1
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1answer
62 views

Why does domain size change results of NDSolve? / How to overcome this?

this is a follow-up on a previous question which was answered, but it turned out that I was running in circles... I have the following code: ...
2
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1answer
60 views

Problems with Neumann (zero flux) boundary conditions

I have the following code: ...
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0answers
28 views

Manipulating a One-Dimensional Plot of ParametricNDSolveValue

I am trying to use manipulate with a plot of a numerical solution to a system of two coupled differential equation solved using ParametricNDSolveValue. I have ...
5
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1answer
708 views

Solve PDE with DiracDelta function

This question is related to Analytic solution of dynamic Euler–Bernoulli beam equation with compatibility condition. I think it is more appropriate to open another question on this topic. In the ...
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1answer
57 views

How to solve for a Diff Eq? [closed]

Solve the differential equation y'(x) + x * y(x) = 0, where y(0) = 3. Show your solution is correct; that is, plug it back into the original DE and show it works.
3
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1answer
90 views

Solving a stiff nonlinear ODE system

The system I am trying to solve is simple, but looks pretty stiff and I have unsuccessfully tried to solve it with StiffnessSwitching. It is the following one: <...
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1answer
48 views

Elimination of numerical error in initial data

Elimination of numerical error in initial data can be crucial for its subsequent evolution. In the following simple example ...
2
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1answer
43 views

TemporalDiscretization in MethodOfLines

When solving ODE's one can use options like MaxStepFraction to control the number of grid points. When solving PDE's ...
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1answer
97 views

Partial differential equation - DSolve gives no output, but solution exists

I have trouble obtaining solution for equation using DSolve: My mathematica code is given by: ...
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0answers
51 views

problem of NDSolve with solving a simple BVP

I'm trying to solve a simple BVP of the following equation $-10.625 + 16.75 u - 7.5 u^2 + u^3 + 4 e^{0.5(u-2.5)^2}f''(u) = 0$ on the interval of $[0,5]$ with boundary conditions $f[0]=0$ and $f[5]=...
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1answer
81 views

Solving system of PDEs with NDSolve

I am trying to solve a system of coupled PDEs with zero-flux boundary conditions on a large domain. I have two problems: 1) Is there a possibility to use results of NDSolve as inititial conditions? ...
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0answers
40 views

Plotting the solutions of parametric NDSOLVE[] as a function of its parameters

I am trying to solve a 2 set of coupled differential equations one using parametricndsolve and other using *ndsolve . So far I am successful in solving these equations. The solution I found by using ...
5
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1answer
140 views

One dimensional heat exchange on a ring: Periodic solution

Subsequent I consider the transient heat exchange problem of a ring in polar coordinates. The ring is heated in a small range 0<\[CurlyPhi]<20° and cooled ...
0
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1answer
64 views

Solving a system of linear differential equations [closed]

I am trying to solve a system of linear differential equations, and I am following the instructions given on the Wolfram Alpha page. I am not getting the desired output, as can be seen below: In the ...
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1answer
47 views

Solution of non linear coupled equations by using shooting, block and StartingInitialConditions

My code is not giving out put. Moreover i do not know how to copy paste this code from my note book. is there any easiest way to paste here. I m plotting graph for the different values of R. I have ...
3
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1answer
153 views

How to Solve $y'(x)=x\ln(y(x))$ with $y(1)=1$ using DSolve

The solution to $y'=x \ln(y)$ with initial conditions $y(1)=1$ is $y=1$. How to persuade DSolve to obtain this solution? ...
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0answers
46 views

Solving coupled differential equations with 4 unknown constants

Recently I just started Mathematica for solving differential equations. Then I tried following 7 coupled differential equations with four unknown constants $ (a, b, c, d) $. But after completion of ...
7
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2answers
522 views

Finite element heat conduction with coupled 1D and 3D equations

I would like to perform a 3d FEM transient heat transfer in fluid and solid, which should have also included fluid dynamic simulation. But I want to simplify it into a 3d FEM without fluid dynamic ...
3
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1answer
86 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
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0answers
70 views

Solving 2D Integro-Differential equation numerically

The following problem was given to me by a friend, so I can't really guaranty that a solution exists, but if, I certainly can't find it myself... Let us consider the following Integro-differential ...
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0answers
45 views

NDSolve 1/0 error

I'm having trouble to solve a differential equation with NDSolve. Does anyone knows how can I get rid of this problem? ...
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0answers
36 views

DSolve 4 variables function error

Mathematica version: 12.0.0.0 I'm trying to solve 2 basic differential equations; ...
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2answers
75 views
0
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0answers
70 views

Using ParametricNDSolve for coupled differential equations

I am trying to solve two coupled equations. I have one parameter, namely c, in the program given below. What I am trying to find is the solution for the coupled ...
9
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1answer
187 views

Finite element for coupled 1D and 3D equations

This is a renewed post for this question, since the old post is already 2 years old and the problem hasn't been solved completely. The problem is to solve heat conduction with robin type boundary ...
5
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1answer
127 views

Understanding PeriodicBoundaryConditions

Every thing works fine in a simple example with periodic boundary condition u[ 2,y]==u[0,y] from documentation of ...
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1answer
75 views

Why does trying to plot the solution to this system of ODEs this way lead to errors?

I would like to plot the curve $\alpha(s) = (l(s), h(s))$, where $l$ and $h$ are the solutions to the system $l'^2 + h'^2 = 1$ and $l'h''-l''h'=h'\tan(l)$. Here's what I tried: ...
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1answer
77 views

Help me to fixe the errors in my code [closed]

This code does not give me the expected plot, so please help me. ...
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0answers
383 views

I am having trouble solving a nonlinear ODE with Homotopy Analysis Method using BVPh2 package on Mathematica

I have the following equations after performing the similarity transformation on fluid dynamic equations. $f'''+ff''-2f'^2-Mf'-G_rg=0\\(1/P_r)g''+g'f-Rg + \delta Exp[g/(1+\epsilon g)]=0 $ I have 5 ...
3
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0answers
235 views

Solving nonlinear PDE in Mathematica [closed]

I want to solve the nonlinear PDE for the anisotropic fluid flow: $(C_{ijkl}v_{k,l})_{,j}-p_{,i}-v_jv_{i,j}=0$ Mathematica can solve it without last nonlinear term with the following code (using ...
3
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3answers
1k views

Using periodic boundary conditions in NDSolve

I need to solve a 2D linear elliptical equation in polar coordinates using NDSolve, but I can’t seem to get Mathematica to accept the required periodic boundary conditions. My actual differential ...
1
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1answer
62 views

NDSolve: Boundary conditions not numerical

I am trying to solve coupled differential equations using NDsolve. I am getting an error which says Boundary conditions not numerical. I am not sure about my mistake. Can I get some help? My code ...
3
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0answers
84 views

How do I truncate an interpolating function?

I have a very large interpolating function and want access the function at one point in time. I am running out of RAM running ...
3
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1answer
82 views

Using ParametricNDSolve with n subscripted functions

I want to calculate trajectories of an n-pendulum. For the number n=1 it's just a pendulum, for n=2 a double pendulum , for n=3 a triple and so on. The Solver has to solve n equations for the angle. ...
2
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1answer
161 views

Solving multi-field problems in MMA 11.3

Based on the PDE model proposed by @Schumacher Solving a second order coupled PDE system, the one dimensional multi-field Problem I would like to solve such benchmark test: namely: u(x): ...
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0answers
50 views

How to apply the utility Packages for Numerical Differential Equation Solving

I have solved two coupled equations with {Solf, Solg} = NDSolveValue[eqns, {f, g}, {x, 0, L}, {t, 0, tmax}] and want to extract the computational grid ...