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

learn more… | top users | synonyms (3)

1
vote
0answers
198 views

Wave equation PDE with changing boundary condition [closed]

This is my first post here, normally with mathematica I will solve out the PDE using eigen function expansion or separation of variables and then model the solution in mathematica. However this time I ...
1
vote
1answer
83 views

Optimization of the solution to an ODE

Apologies if this is obvious -- I'm very new to Mathematica. I'm trying to minimize the solution to an ODE with respect to a variable. The following code generates the solution to the ODE, ...
2
votes
1answer
78 views

Why does NDSolve and NIntegrate not give the same result? [closed]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
5
votes
1answer
150 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
55 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
49 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
69 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
67 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
72 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)\...
2
votes
0answers
46 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
votes
1answer
92 views

Sine curve arc length

...
1
vote
0answers
54 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
vote
0answers
45 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
81 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
votes
0answers
43 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
votes
0answers
40 views

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

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
46 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
359 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
votes
1answer
131 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
votes
1answer
83 views
6
votes
1answer
172 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^...
0
votes
0answers
52 views

What I make wrong with Module command;

I have a differential equations that I have to solve in two parts.e.g: ...
0
votes
0answers
55 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
79 views

NDSolve DAE solution order is mixed up

Compare the two solution sets below: in the first one (x == False), there are only 3 dependent variables while in the second one (...
0
votes
0answers
47 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
38 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
votes
0answers
75 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
votes
2answers
38 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
92 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 ...
0
votes
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
153 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
86 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
128 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
74 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
3
votes
0answers
88 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
145 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
112 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
votes
0answers
41 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
116 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 ...
5
votes
0answers
157 views

Dealing with a nonlinear PDE using FEM

As far as I can see in the Mathematica documentation center, there are no built-in ways for solving nonlinear PDEs using Finite Element Method (FEM). I am dealing with a simple nonlinear time-...
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?