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

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system of differential equations 3 DSolve [closed]

dS/dt = a - dS - λ S I + β R dI/dt = λ S I - (d + m)I dR/dt = m I- (d + β)R Solve the above equation and plot the curve.
3
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1answer
162 views

How can I combine NDSolve[] with NSolve[]

Consider the two below ODEs with following dependent B.C. In the boundary conditions $k$ is an unknown. $$y_1''(x)=x$$ $$y_2''(y)=0$$ $$y_1(1)=y_2(1)$$ $$y_1(-k)=y_2(-k)$$ $$\frac{\text{dy}_1(1)}{\...
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0answers
49 views

Any possible to save a 'partial' result of NDSolve when it was aborted due to insufficient memory?

I have run a NDSolve code for an extremely long time. Unfortunately, it was aborted because there was insufficient memory available to complete the computation. At ...
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1answer
203 views

How to pass arguments in NIntegrate and NDSolve

I am solving PDEs with NDSolve and NIntegrate, but I do not know how to pass arguments correctly. My orignial code is very ...
0
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1answer
116 views

Plotting Limit Cycle

I have Lotka Volterra Equations where the prey equation is modified. The Equations are x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t] y'[t]=-c*y[t]+d*x[t]*y[t] To plot the ...
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0answers
57 views

Numerical fitting trajectory to model that has NDSolve

I have a model which describes the motion of an object on a plane. ...
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0answers
52 views

Double Integral with NDSolve!

I have fivefold multiple integral and I wanted a speed calculations.I came across on this Question and had already begun the problems. Here is a toy example with simple double integral: ...
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0answers
105 views

Fitting Three-Dimensional Data with Parameters

I have been trying to fit a model of rate equations to data of three dimensions. The rate equations in my model are as follows. ...
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2answers
66 views
1
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1answer
45 views

PolarPlot with InterpolatingFunction not working?

So I have solved a PDE with NDSolve which returns h -> InterpolatingFunction. I can happily plot the results with ...
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1answer
59 views

Diffusional equation [closed]

I am still new to Mathematica. I'm trying to solve a diffusional equation ...
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1answer
56 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
55 views
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1answer
58 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 ...
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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 ...
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0answers
38 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
78 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 +...
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1answer
49 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 ...
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1answer
51 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 ...
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 ...
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1answer
56 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 ...
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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. ...
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0answers
49 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)^...
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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
64 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 ...
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0answers
31 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\...
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1answer
57 views
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1answer
73 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." <...
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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 ...
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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
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1answer
127 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
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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, ...
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0answers
34 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...