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

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3
votes
0answers
52 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let ...
0
votes
1answer
26 views

Coupled differential equations — singularity being reached very quickly

I was wondering if there was a way to help the solutions to these differential equations not hit a singularity as quickly as they currently do. The equations are very complex (derived from a ...
4
votes
1answer
30 views

Solve a time-dependent matrix DE using NDSolve

I am trying to numerically solve a time-dependent matrix DE using Mathematica. However, it seems that Mathematica freezes even for two-dimensional matrix equations. For example, we have: ...
1
vote
1answer
58 views

Trouble solving a system of partial differential equations

I am trying to solve a system of linear PDEs analytically and I dont get the answer. I am new to this tool, appreciate your help ...
1
vote
2answers
84 views

How to determine the parameter in a differential equation with some fixed solution

Assuming that I have a ODE system with undetermined parameter $$x''(t) == y(t) x(t)$$ $$y'(t) == 2 - a x(t)$$ and I have some fixed solution condition $$x(0)=0$$ $$x(10)=8$$ $$y(10)=3.5$$ Is there ...
0
votes
0answers
23 views

How to solve PDE in 2D region with mixed boundary condition?

I'm trying to solve the inhomogeneous wave equation with mixed boundary conditions. How do I input these conditions? Is is still with NDSolve?
2
votes
1answer
46 views

Using ouput of ParametericNDSolve as argument in NMinimize: NMinimize::nnum: function value not a number

I am trying to fit some experimental data and I am trying to use NMinimize function to calculate the parameters that fit the experimental dataset. I am also using ...
9
votes
1answer
119 views

MMA breaks down when `DSolve` -ing a third-order linear ODE

My code is: DSolve[y'''[x] + (x^3 + a^3) y[x] == 0, y[x], x] It should be noted that similar code not only meets the similar problem but also returns more ...
3
votes
1answer
54 views

NDSolve: obtain time difference when different solutions get same distance to equilibrium value

I have a numerically solved a differential equation which has an equilibrium value and a starting point, both included as a parameter. I want to plot the difference between the times it takes to come ...
3
votes
1answer
94 views

EquationTrekker using Mathematica 10.2

I wonder whether the problem that arise with the following code is specific to my machine, as it seem to work with the documentation example. ...
1
vote
1answer
800 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
0
votes
1answer
70 views

NDSolve There are fewer dependent variables, {V[S,t]}, than equation

I am trying to solve the BlackScholes PDE for Barrier option. It works fine for european barrier, but errors out on american boundary condition ...
0
votes
0answers
107 views

How to solve the heat flow PDE for the constant source term

I have the two dimensional heat flow equation solved for a two dimensional reagion over time. That is an instance I found in the internet. What I am looking for is a method how to determine the heat ...
13
votes
3answers
4k views

Find all roots of an interpolating function (solution to a differential equation)

I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This ...
2
votes
1answer
61 views

Decouple 3 simultaneous 2nd order ODEs (of 3 dependent variables)

I have three simultaneous ODEs with coupled dependent variables. I was wondering whether there's a way for Mathematica to decouple these equations (into three ODEs of a single dependent variable ...
10
votes
1answer
129 views

“ParametricSensitivity” in ParametricNDSolve

"ParametricSensitivity" is listed as a Method in the documentation for ParametricNDSolve, ...
0
votes
0answers
60 views

Error with ND Solve [on hold]

I am new to Mathematica, and I am having some issues solving a homework problem of a differential equation. Here is the code: ...
3
votes
1answer
145 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
9
votes
1answer
763 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
0
votes
0answers
44 views

Solve ODE with constraints [on hold]

I'm trying to add constraints to my system of ODE, given by simple inequality: E1 > 7 and E2 > 7. ...
0
votes
0answers
5 views

Coupled partial diffential equation, with boundaries specification [migrated]

Please, help me to find a books or samples to learn how to solve such coupled equations $$\frac{\partial T_1(x,t)}{\partial t}&= \alpha_1 \frac{\partial^2 T_1(x,t)}{ \partial x^2} +f(x) ...
0
votes
2answers
129 views
0
votes
1answer
106 views

How to make the plot smooth

There are some stranges point which cause the figure isn't smooth. I think that the reason is the method of numericial integration. Here is my code, it's pleasure that one can revise the drawbacks in ...
0
votes
0answers
55 views

Piecewise NDSolveValue: Nested Variable Iteration

I am attempting to make the variable Rc a piecewise-function of [z] and have it update as NDsolve iterates through the range of 'z' such as {z,0,Le), but to no avail. The following code is an attempt ...
2
votes
1answer
65 views

Simplifying the result of DSolve

I have a system of differential equations that can be solved with DSolve. However, the coefficients are very long there are like terms which can be combined. I used //FullSimplify in my code but the ...
-1
votes
1answer
116 views

Problem with NDSolve and If

If T=T1, program can calculate. But, when T = T1*If[Abs[q2[t] - q2d] < e1 && Abs[q2'[t]] < e1, 0, 1], program can ...
0
votes
1answer
31 views

Using NDSolve initial conditions as parameters for a function and then a replacement rule

I am trying to make a function based on two initial conditions of a set of differential equations: ...
4
votes
1answer
267 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
0
votes
0answers
82 views

How to remove error at large time in NDSolve

I am working with solutions of a linearly damped wave equation. In the following code I use a "transparent" boundary condition at the end, which allows waves to pass through the specified boundary so ...
0
votes
0answers
39 views

How to plot multiple numeric ODE solutions in phase space [on hold]

I have a system of four coupled ODEs whose solution (and solution process) are sensitive to the value of a parameter $a$. $$\bar X '(t)=\bar F(\bar X, t, a)$$ If possible, I would like to create a ...
0
votes
0answers
79 views

Calculating 15 coupled differential equations [on hold]

I have 15 coupled differential equations linear in time that need to be solved. Rewriting the equations in a matrix form, they can be expressed following as a single equation, $\frac{d ...
-2
votes
0answers
43 views

How to assign values to constants inserted in a solution by DSolve [on hold]

I am trying to solve first order ODE with DSolve, but it didn't pan out. How can I solve for the inserted variable K[1]? Your ...
1
vote
0answers
46 views

Solving an ODE using shooting method [duplicate]

I have been trying to solve the following nonlinear ordinary differential equation: $$-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0$$ with boundary conditions ...
2
votes
0answers
363 views

Solving two-component two-dimensional differential Equation with NDSolve (Brusselator Model)

I'm trying to solve a two-component two-dimensional reaction-diffusion differential equation system with Mathematica. The background of the model is the so called "Brusselator Model" where one can ...
2
votes
0answers
34 views

Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
0
votes
1answer
95 views

Nonlinear differential equation: numerical solution

I have to find and plot a numerical solution for this second order differential equation: u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0 where 0 <= x ...
0
votes
1answer
60 views

DSolve Error 3D Navier Stokes (z,r,t)

I am essentially wanting to solve Navier Stokes in the [z,r,t] dimensions (2D+Unsteady Flow) for pressure driven flow. However, I keep getting an error I am unable to resolve in my Dsolve such as: ...
1
vote
2answers
62 views

Condition on Inside of Region

How do I handle boundary conditions present in the region. Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this ...
1
vote
1answer
96 views

ODE of an eccentric circle

How can we simplify the solution in: DSolve[ {Sqrt[ 1 - (r[t] - T^2/r[t])^2/(2 a)^2]/(r[t] - T^2/r[t])/(2 a) == r'[t]/ r[t], r[0] == T}, r, t] (r,t) are polar ...
1
vote
1answer
57 views

How do I restrict the range of an interpolating function in NDSolve?

I have a numerical solution for a differential equation. I know that the gray dotted solution is unphysical. Is there a way I can tell mathematica to ignore the gray dotted solution (e.g. restrict the ...
8
votes
1answer
179 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ ...
0
votes
1answer
69 views

How to solve time dependent coupled differential equations? [closed]

I am trying to solve time dependent coupled differential equations with know initial conditions. I am just a beginner in terms of coding so would really appreciate if someone can give me an example of ...
1
vote
1answer
97 views

How can I use NDSolve with a variable parameter?

I'm a new user and I can't understand how to solve this function for variable values of vr (for example vr from 0 to 5 in steps ...
3
votes
0answers
712 views

Solving a diffusion equation

I need to solve a particular diffusion equation with NO boundaries (see eqn. (2.10) in: Ann. Rev. Astron. Astrophys. 19:137-62 (1981).) with nu = cost. ...
1
vote
1answer
42 views

Getting the message NDSolve::underdet:

I am solving the wave equation with initial position and velocity function: ...
0
votes
1answer
59 views

NDSolve does not satisfy initial conditions

For the problem I'm facing, I have three coupled diff eqns that I'm trying to solve ...
0
votes
1answer
81 views

Improving NDSolve computation speed for 3D stationary PDE

Continuing my last question, I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). The analytical solution for this equation is ...
0
votes
2answers
85 views

How to solve a pair of coupled 2nd order equations using shooting method

I have a pair of equations for x[t] and y[t]. Both are 2nd order and they are coupled. Now say that I know the following ...
0
votes
2answers
127 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
0
votes
0answers
132 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. The equation below presents the final form ...