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

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1answer
55 views

Can I solve system of differential equation in a matrix form?

I'd like to solve simple system of differential equations: x'[t] == 6x[t] - 6y[t], y'[t] == x[t]-2y[t]; but I want to avoid formulas like DSolve[{x'[t] == 6x[t] - 4y[t], y'[t] == x[t]-2y[t]}, {x,y},...
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1answer
53 views
0
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1answer
57 views
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0answers
22 views

How many boundary conditions are required for two coupled Non-linear ODE in two variables?

I'm using NDSolve to solve the following two coupled Nonlinear ODEs in two variables: Equation1 = Equation2 = It can be seen that the level of nonlinearity is very high. I have solved the ...
0
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2answers
44 views

Produce several file outputs within one calculation

I have a differential equation which I solve with NDSolve. With the obtained solution I calculate some quantity. Then a constant in the ODE will be raised (until a ...
1
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0answers
35 views

Looking under the hood of DSolve

Is it possible to print out information about the algorithms DSolve uses to solve a differential equation? I'm looking for something similiar to this Maple procedure. It lets you specify how much ...
2
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1answer
77 views

Using loops to draw multiple polygons and discretizing them

I am trying to plot the first eigenvalue of the Laplacian operator with zero Dirichlet condition on following figure against decreasing values of $\varepsilon$. I used ...
3
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1answer
55 views

Why does the Part::partw error appear when using DSolve?

I solved the following ordinary differential equation for $F(x)$ using DSolve in Mathematica $$ \begin{align} \begin{split} & A x^2 (x^2 + 1) F'''(x) - \left(3 A (b - 2) x^3 + a x^2 +A (b - 2)x +...
1
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1answer
48 views

Using NIntegrate inside NDSolve

I need to use NIntegrate inside NDSolve, for example: ...
3
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0answers
57 views

Two questions about “wraparound” with “Event” method

I am learning EventLocator method from the document center. As for the following code (copy from this document) solving the sine-Gordon equation, it uses the ...
0
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1answer
50 views

Solving boundary-value problems within a specified region

Is it possible to use DSolve with non-initial boundary conditions? For example, eqn = a == b x'[z] + c x[z] over the region 0 to L, something like ...
0
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1answer
57 views

NDSolve error: Step Size is effectively zero; singularity or stiff system is suspected

my current project is numerically solve the Friedmann equation: (a-dot / a)^2 = H_0^2 (sigma_r / a^4 + sigma_m / a^3 + sigma_lambda + simga_k / a^2) What I did was split my equation into two ...
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0answers
40 views

NDSolve failure, probabily discontinuity problem [closed]

I'm trying Mathematica this week and I would like to solve numerically a system of differential equations. It works with a simple problem, but since it is an economic problem, I need the profit ...
2
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0answers
81 views

Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
0
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1answer
54 views

Writing PDE boundary conditions with derivatives, More general than Neumann

I am solving 2D Laplace equations on f[x,y] with boundary conditions SomeVector[x,y].Grad[f] == 0 This is more general than Neumann. Is there a way to set such boundary conditions for a curved ...
1
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1answer
102 views

Euler-Bernoulli cantilever beam with parabolic load

How do I obtain the displacement in the free end of a bar with Parabolic load (I.e. in point with length L)? I found the information on a site, but only I found for uniform load. Someone who ...
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0answers
41 views

Behavior of solution to a ODE near a singular point [closed]

I want to see how the solution to the following ODE looks near z=z0. ...
1
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0answers
48 views

Vinculated boundary conditions [closed]

I have a problem in the form: $-y''(x)+V(x)y(x)=0 $ with the initial conditions: $\quad y'(0)=k \ y(0), \quad k=cte$ The $V(x)$ is a model's parameter, for example $V(x)=\frac{6}{\left(x+2\right)^...
0
votes
1answer
55 views

function definition, $ symbol apparition after variables [closed]

I have a proble with a system of two differential equations ...
4
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1answer
52 views

How to use `Abs` within `Event` with a function of several variables?

I would like to use EventLocator to stop NDSolve with the Event command ...
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0answers
31 views
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0answers
50 views
0
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1answer
30 views

DSolve with coefficients and assumptions

The command below: DSolve[{s'[t] == l t, s[0] == 0}, {s[t]}, {t, 0, a}] gives the error DSolve::alliv: The function <...
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0answers
52 views

NDsolve memory leak

Every time I run NDsolve it uses some memory that I am not able to free later. The following is an example code based on the spring equation (Hooke's law) that ...
1
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0answers
30 views

Setting different B.C. for different fields in NDSolve

My question regards construction of a PDE solver for several fields, with different type of boundary conditions for several fields. Say I have the following set of equations: $$ \partial_{t}\rho+v\...
1
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1answer
57 views
0
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1answer
71 views

Lagrangian for Spring-Pendulum [closed]

I solved a Spring-Pendulum System with NDSolve. I tried to plot a graph with the interpolated data but always returns a message "An improperly formatted directive with head Symbol was encountered." <...
1
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0answers
52 views

PDE: Specify AccuracyGoal, StepSize, and WorkingPrecision interval-wise [closed]

I am using Mathematica 8. I have two ODEs (in time) and a diffusion PDE (in radius and time) which are all coupled to each other. I solve them using NDSolve by ...
1
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1answer
41 views

numerical values for the solution of NDEigensystem

I tried to solve Schrödinger equation in 3D box using the NDEigensystem. My code is: ...
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0answers
76 views

Power Spectral Density Plotting [closed]

I am new to signal processing.I am analyzing the connection between the behavior of the Rossler model and its parameter c. \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ \label{eq:...
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2answers
93 views

Stiff second order ODE

I am trying to solve numericaly $f''=f^{3}-f$, exact solution is Tanh(x). Problem is numerical solution fails if i coming closer to tanh plateau. StiffnessSwitching method dont help. ...
1
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1answer
68 views

Nonlinear Markov chain (numerical simulation)

Suppose you have a linear Markov process, and you can write it as x(t+1) = Ax(t). Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ...
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0answers
4 views

Isothermal coordinates [migrated]

Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E∗(du^2+dv^2)$ and where $E>0$ is an harmonic function? I know that this metric is a special kind ...
2
votes
1answer
126 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. $y''+\frac{3}{x}y'-...
3
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2answers
156 views

Is it possible to assign numbers generated in an Error-Message?

If I have a differential equation of the form ...
0
votes
1answer
67 views

Stopping NDSolve when encountering stiffness

I am solving a differential equation for different initial conditions using ParametricNDSolveValue. I need to look at the value of the solution at some later point, ...
1
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0answers
33 views

Speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions

I have a question on speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions. I build the ODE system with NDSolve...
0
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0answers
80 views

Error - Differential equation //2

This is a follow-up question, since it relates to the solution of a modified version of the original differential equation discussed here: Differential equation: NDSolve::berr I receive an error ...
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0answers
60 views

Differential equation: NDSolve::berr

I'm trying to solve the following differential equation. I'm able to obtain a solution, and that solution looks more or less as how the theory predict it should be. ...
1
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2answers
56 views

Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

How do I plot an ParametricPlot with the x-axis using an logarithmic scale? Since I need to use an ParametricPlot, I can not use the LogLinPlot[] and I also was not able to find any viable Solution in ...
1
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1answer
71 views

Differential equation involving history integral

I have not found a solution by using google so I hope I can ask this here. I have an issue with a problem I am trying to solve and I was wondering whether what I am doing is not possible with ...
0
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1answer
57 views

Solution of Coupled second-order ODEs and plot the diagram

We have two second-order Coupled differential equations as the followings: $$\left\{\begin{array}{lr} \displaystyle \frac{{{d^2}{y_1}}}{{d{x^2}}} = \{ \frac{{\sqrt {\frac{{1 - {\varepsilon ^2}}}{{{{(...
1
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0answers
196 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
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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
149 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
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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: ...