# Tagged Questions

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

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### Issues with modeling pulses in a very simple system of DAEs

Bug introduced in 10.4.1 or earlier Bug has been confirmed by WRI [Case:3594387]: It does appear that the NDSolve function is not behaving properly in this case and an incident report has been ...
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### Using NIntegrate inside NDSolve

I need to use NIntegrate inside NDSolve, for example: ...
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### 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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### 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 ...
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### function definition, $symbol apparition after variables [closed] I have a proble with a system of two differential equations ... 1answer 53 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 ... 0answers 32 views ### Problem with ParametricNDSolve and FindMaximum [closed] I have a system 4 coupled differential equations: ... 0answers 53 views ### Solving 4 coupled differential equation and minimizing the solution I have a system of$4$coupled differential equations. ... 0answers 70 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 ... 0answers 32 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\... 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 ... 1answer 61 views ### Need help Solving Taylor-Maccoll Equation ... 1answer 79 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." <... 1answer 46 views ### numerical values for the solution of NDEigensystem I tried to solve Schrödinger equation in 3D box using the NDEigensystem. My code is: ... 1answer 132 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'-... 2answers 95 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. ... 0answers 77 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:... 1answer 71 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, ... 1answer 68 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, ... 2answers 157 views ### Is it possible to assign numbers generated in an Error-Message? If I have a differential equation of the form ... 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 ... 0answers 213 views ### DSolve versus DSolveValue [closed] I've just discovered the new command DSolveValue in Mathematica 10. Is this new command now the preferred instead of DSolve? Is ... 0answers 36 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... 0answers 64 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. ... 2answers 63 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 ... 1answer 73 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 ... 2answers 333 views ### Lagrangian to Hamiltonian I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ... 1answer 59 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}}}{{{{(... 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: ... 1answer 84 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, ... 1answer 324 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 ... 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. ... 4answers 417 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 ... 1answer 77 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 ... 1answer 160 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: ... 1answer 82 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 ... 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: ... 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 ... 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: ... 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 ... 1answer 201 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^...
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)\...