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

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2
votes
1answer
61 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: ...
0
votes
1answer
64 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, ...
-4
votes
0answers
56 views

How to solve and draw the phase portrait of a linear system [on hold]

How to solve and draw the phase portrait of this linear system $\frac{dx}{dt}=Ax$ where $A=\begin{bmatrix}{0}&{2}&{0}\\{-2}&{0}&{0}\\{2}&{0}&{0}\end{bmatrix}$
1
vote
0answers
38 views

Wave equation PDE with changing boundary condition

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 ...
4
votes
1answer
298 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
-2
votes
0answers
30 views

How to solve nonlinear system of four PDE

DSolve[{D[Subscript[g, 11][u, v, t], t] == -2 [Psi][u, v, t] Subscript[L, 11][u, v, t], D[Subscript[g, 22][u, v, t], t] == -2 [Psi][u, v, t] Subscript[L, 22][u, v, t], D[Subscript[L, ...
0
votes
0answers
60 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. ...
3
votes
4answers
414 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
3
votes
0answers
63 views

Solving a matrix differential equation using RBFs

Michael Kelly in the paper http://www.mathematica-journal.com/2010/02/evaluation-of-financial-options-using-radial-basis-functions-in-mathematica/, discussed how to apply Mathematica for solving the ...
1
vote
1answer
60 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 ...
5
votes
1answer
129 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: ...
2
votes
1answer
64 views

Why does NDSolve and NIntegrate not give the same result?

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 ...
1
vote
0answers
50 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
1answer
52 views

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

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 ...
1
vote
2answers
60 views

Plotting the InterpolatingFunction from NDSolve [on hold]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
2
votes
2answers
45 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 ...
5
votes
1answer
120 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 ...
1
vote
1answer
63 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 ...
1
vote
1answer
71 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 ...
2
votes
0answers
43 views

Solution of the Lagrange's minimal surface equation [on hold]

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
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) ...
1
vote
1answer
83 views

Discontinious Boundary condition NDsolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $U[0,y,t]=0, if, 0<y<1, ...
3
votes
1answer
204 views

NDSolve mixing many scalar and vector equations

I have a set of scalar equations in many unknowns, which I want to combine with a vector equation inside an NDSolve. The equations are a mix of differential and algebraic equations. A set of scalar ...
0
votes
0answers
34 views

Why am I getting an error message from NDSolve? [closed]

The error message is: {NDSolve[<<1>>,{y,z},{t,0,25}]} is neither a list of replacement \ rules nor a valid dispatch table, and so cannot be used for \ replacing. ...
1
vote
0answers
37 views

NDSolve with only discrete variables

Is is possible to use NDSolve with DiscreteVariables if there are no continuous-time variables? This fails: ...
2
votes
1answer
118 views
0
votes
0answers
36 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\\ ...
1
vote
1answer
41 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
45 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 ...
0
votes
0answers
27 views

NDSolve and Nintegrate give different plots of the same function? [closed]

So my problem is that I transformed a differential equation to an integral equation and the results from Nintegrate is different from what I get with NDSolve. Shouldn't it be the same? I was expecting ...
0
votes
0answers
53 views

Numerical solution and solution via Fourier series do not match

I am trying to solve the following system of DE $$\left( \begin{array}{ccccc} 3.21539 k & 0 & 0 & 0 & 0 \\ 0 & 4. k & 0 & 0 & 0 \\ 0 & 0 & 6. k & 0 & ...
5
votes
2answers
355 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 ...
0
votes
1answer
48 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: ...
10
votes
3answers
4k views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
4
votes
1answer
1k views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
2
votes
1answer
154 views

The numerical solution of a nonlinear ODE: boundary value problem

I want to solve the following nonlinear ordinary differential equation with boundary values $f(0)=1$ and $f(1)=1$: $${\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left( x \right) ={\dfrac { \left( 51-51\,x ...
0
votes
0answers
54 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
70 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
48 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
43 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
35 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
2answers
35 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 ...
1
vote
1answer
143 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 ...
2
votes
1answer
88 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
1answer
192 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 ...
0
votes
0answers
85 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 ...
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 ...
1
vote
1answer
130 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in ...