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

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5
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1answer
161 views

Transcritical Bifurcation phase portraits

An example equation for a Transcritical Bifurcations is given by: $$\dfrac{dx}{dt} = f(x, r) = r x - x^2$$ In Mathematica, we can define the function as: ...
1
vote
2answers
75 views

Plotting the InterpolatingFunction from NDSolve [closed]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
1
vote
1answer
56 views

How can use Table for two functions obtained from NDSolve? [closed]

I have obtained a numerical solution using NDSolve for two functions a(x) and b(x). how do I use Table to make a list of a(x) vs b(x) values. is it simply Table[{a(x),b(x)},{x,0,100}] or should I use ...
2
votes
2answers
53 views

Difficulty finding roots of an interpolation function from NDSolve

I have been trying to find the point at which one of the solutions of a system of two ODEs crosses zero. I used the method suggested in this answer to a previous question, which seemed to be the most ...
1
vote
1answer
79 views

How to solve different PDE defined in different regions coupled through boundary condition

I would like to solve two different partial differential equations each one defined in a different region and in different coordinates. However the equations are coupled through a boundary condition ...
2
votes
1answer
72 views

Will the solution NDSolveValue finds outside of the region I give it give me bogus results?

I'm using NDSolveValue to solve Laplace's equation for a relatively simple system. I have two rectangles, separated by a small gap, which I define using RegionDifference: ...
1
vote
1answer
74 views

NDSolve a system of PDE's when one variable does not have an explicit time derivative

Say I want to solve the following set of PDE's (my actual equations are way more complicated, this is just a simplified example to show the structure): $$\begin{align} \partial_t f(x,t)&=1-g(x,t)\...
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0answers
49 views

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: ...
0
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1answer
94 views

Sine curve arc length

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0answers
62 views

NDSolve returns solution with single point domain

Thanks to helpful comments from Michael E2 and George2079, I was able to focus in on exactly the source of the issue. With some simplification, I can reduce the problem to: ...
1
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0answers
46 views

NDSolve with only discrete variables

Is is possible to use NDSolve with DiscreteVariables if there are no continuous-time variables? This fails: ...
1
vote
1answer
83 views

Parametric Plot from ODE using WhenEvent

I am searching for a while now, but I don't seem to be able to find an Answer for my Problem - if I am just not able to search properly, I am really sorry. I Simplified my Problem to the following ...
0
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0answers
48 views

Solving a 2 dimensional differential with NDSolve, Dirichlet boundary condition

I've tried to solve the following system of equations: \begin{eqnarray} f(x,y)=\lambda^2 \nabla^2 f(x,y)\\ \frac{\partial f}{\partial x}(0,y) =0\\ \frac{\partial f}{\partial y}(0,y) =A\\ \frac{\...
0
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0answers
42 views

How to handle a special Neumann-like boundary condition in this coupled 2 order differential equations? [duplicate]

How can I solve this problem using Mathematica? I have typed like this(s=0.25δ^4) ...
0
votes
1answer
47 views

Find numerical solution to this system of DE

I am trying to solve this system $$\left( \begin{array}{ccccc} 2 k & -k & 0 & 0 & 0 \\ -k & 2 k & -k & 0 & 0 \\ 0 & -k & 2 k & -k & 0 \\ 0 & 0 &...
1
vote
1answer
48 views

How to set MaxStepSize for spatial variable in NDSolve?

When applying NDSolve to a 1-D transient heat equation, the following code appears to set MaxStepSize for the temporal variable t. ...
0
votes
1answer
49 views

Errors only when code is iterated

Hello I'm trying to have two for loops sweep two parameters and for each 2-tuple of those parameters I want to solve a differential equation. To do this I have the following code: ...
5
votes
2answers
360 views

How to write a code to solve my ODE problem?

I have the ODE: $$y''+\lambda y = B^3\sin^3(\sqrt{\lambda}x) \ y(0)=0, \int_0^1 y(x)\sin(n\pi x)dx=0$$ I am not sure how to write the mathematica code to solve this ODE, obviously I need here DSolve ...
2
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1answer
133 views

How can I fit cyclic experimental curve with a couple of differential equations?

I have an experimental cyclic curve which looks like this: ...
3
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1answer
92 views
6
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1answer
203 views

How to use NDSolve with moving boundary conditions?

So I am trying to solve the movement in space and time of a spreading gravity current. The interface satisfies the following PDE: $ \frac{\partial h}{\partial t} = \frac{\partial}{\partial x}\left(h^...
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0answers
53 views

What I make wrong with Module command;

I have a differential equations that I have to solve in two parts.e.g: ...
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0answers
56 views

Syntax for Neumann/Robin condition in NDSolve [duplicate]

I can't follow the logic of how a NeumannValue term is to be incorporated into a pde to provide a BC for NDSolve. The ...
3
votes
1answer
99 views

NDSolve DAE solution order is mixed up

Bug in 10.4.0.0, probably introduced earlier. Compare the two solution sets below: in the first one (x == False), there are only 3 dependent variables while in ...
0
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0answers
48 views

Time dependent/dynamic parameter in the system of ODEs

I am wondering what would be the best way how to code the following situation. I have a solution but I don't think it as elegant as it could be. I have a system with 10 ODEs and lot of parameters. ...
0
votes
1answer
39 views

Define inverse Laplace operator as map from functions to functions

I am trying to implement the inverse Laplace operator through P[g_] := h /.NDSolve[{h''[x] == g[x], h[0] == 0, h[1] == 0}, h, {x, 0, 1}][[1]] If I now define ...
0
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0answers
76 views

problem with “Infinite expression”, using NDsolve

Im trying to solve an heat equation with NDsolve but i have got a Infinite expression error(1/0). this is the code. ...
0
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2answers
39 views

Beginners problem, Do Loop, Eigenfunction iteration

I am trying to find the first Eigenfunction of the Laplacian (in 1D), i.e. a solution of $$ u''(x)=k u(x)\\ u(0)=u(1)=0 $$ with minimal $k>0$ (in this trivial example, I actually know the analytic ...
2
votes
1answer
93 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
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0answers
26 views

Implementing more accurate boundary conditions in NDSolve

I want to solve a second order differential equation numerically. The boundary conditions are needed to be imposed at z=0 and at ...
2
votes
1answer
159 views

Plotting Phase Diagram

I have the following problem that I'm sure Mathematica can handle, but it's not working for me! In the following code, I'm trying to replicate the Ramsey Model Phase Diagram. In fact, I want now ...
5
votes
2answers
280 views

Simpler way to type Derivative[1, 0][u][0, x]

Though not unbearable, I always feel a little nervous when typing partial derivatives at a specified place e.g. $u^{(1,0)}(0,x)$, which happens a lot when setting initial/boundary conditions for PDEs. ...
0
votes
0answers
88 views

FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
2
votes
2answers
132 views

How do I solve Schrödinger equation with a piecewise periodic Hamiltonian? [duplicate]

My Hamiltonian is HI(t) = Piecewise[ {{H1, n τ <= t <= (n + 1/2) τ}, {H2, (n + 1/2) τ <= t <= (n + 1) τ}}] where ...
0
votes
1answer
195 views

Using data from NDSolve into a secondary equation

I have this ODE, f''''[y]+Z1*(6 f''[y]*f'''[y]*f'''[y]+3 f''[y]*f''[y]*f''''[y])- N1*N1*f''[y] == 0 subject to boundary conditions ...
2
votes
2answers
78 views

How to simplify a differential equation?

Now I get a differential equation like this: (-1 + x) (1 + x)^2 == (2 (1 + x^2) (1 + x^4))/(-2 x (1 + x + x F[x]) + (-1 + x^3) F'[x]) I want to get the standard ...
0
votes
0answers
46 views

Check if interpolated function passes through a specified region

Is there an efficient way to check if a curve that was obtained as an Interpolating Function (from solving differential equations numerically) passes through a given region? I am solving for two ...
1
vote
1answer
58 views
4
votes
1answer
164 views

ColorBars or PlotLegends for ElementMeshSurfacePlot3D

I want to produce a colorbar legend to the output from ElementMeshSurfacePlot3D (Mathematica 10). The pde was solved using NDSolveValue (FEM pdesolution is the resulting interpolating function) over a ...
1
vote
1answer
146 views

NDSolve with coupled ODE's and unknown singularities

I have two coupled ODEs that I am trying to solve numerically. It appears that there is a singularity in the solution to the equations which I am unsure how to get past. Both functions $\alpha$ and $\...
2
votes
1answer
49 views

Asymptotic Radial Wave Equation

I'm trying to reproduce the following solution to the ODE, $$\frac{d^{2}u}{d\rho^{2}} = \frac{l*(l+1)}{\rho^{2}}u$$ Solution: $$u\left(\rho\right) = C\rho^{l+1}+D\rho^{-l}$$ What I've tried in ...
13
votes
1answer
116 views

Empty WhenEvent action crashes kernel

Bug introduced in 9.0 and persisting through 10.4.1 WhenEvent is new in 9.0. This is an example from the docs, slightly modified (action is wrapped in ...
0
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0answers
43 views

How to use NDSolve for mixed types of several equations?

I have three equations, one is partial differential equation and another two are not. They are just normal algebra equations but coupled with the differential equation. I wanna use NDSolve to get ...
3
votes
0answers
121 views

Mathematica Newmark Optimization

Here is my Mathematica code which implements the Newmark method to solve a equation of motion. The variable "ag" contains the accelerations from an earthquake record. Is it possible to optimize this ...
0
votes
0answers
47 views

Extract stiffness matrix from NDSolve

I am solving a set of ODE equations with NDSolve with more than 25 equations. I was wondering is there any way Mathematica gives me the mass and stiffness matrices?
3
votes
2answers
52 views

Numerically solving coupled ODE's with a parameter as initial condition

i'm currently trying to numerically solve a set of coupled ODE's to obtain the functions p(r), h(r) and m(r) in the range of r1 <= r <= r2 with initial conditions m(r1)=a=const and p(r1)=b=const....
0
votes
2answers
73 views

Using an interpolating solution of NDSolve into an algebraic expression

I would like to use the interpolating solution of NDSolve into an algebraic expression without creating a system of a differential equation and algebraic equation. The example is the following, the ...
1
vote
0answers
73 views

How to speed up NDSolve?

I have a program where I need to iterate NDSolve thousands of times for different configurations of a diffusion problem. The thing is, I only need about 3 digits of accuracy. I looked thru previous ...
0
votes
0answers
62 views

Lyapunov exponent of non-autonomous differential equation

I am trying to calculate the Lyapunov exponent for a non-autonomous system using M Sandri code, but it always shows me error "infinite expression 1/0 encountered". Does anyone know about this? Mr. ...
0
votes
1answer
62 views

Find a independent variable value from the numerical solutions of a system of differential equations

I have calculated the solutions for the following system of differential equations using NDSolve ...