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0
votes
1answer
55 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
0
votes
1answer
68 views

How to chop a complex number?

I'm solving some differential equations by iterating and I want to use Chop to get rid of noice smaller than a certain threshold. However, I found that Chop only "chops" the real part, not the ...
0
votes
0answers
33 views

Plotting NDSolve function in complex coordinates

I have this system of equations: $- \ddot{z} + \frac{1}{g} \frac{\partial g}{\partial z} \dot{z}^2 + \frac{1}{g} \frac{\partial g}{\partial z^*} \dot{z} \dot{z}^*$ =0 , $- \ddot{z}^*+ \frac{1}{g^*} ...
3
votes
1answer
86 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
3
votes
1answer
186 views

How to solve PDE with periodic and anti-periodic b.c.?

I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$ ...
3
votes
2answers
107 views

Complex solutions to ODEs

How do I solve the following IVP problem in Mathematica so that I get real solutions? $Q'(t)=b - \dfrac{Q(t)}{100-t}; \quad Q(0)=250$ I tried the following: $\text{$\$$Assumptions}=b>0;\text{$\$$...
3
votes
1answer
120 views

Complex first-order differential equation

I have a differential equation $\frac{dx}{dt} = \sqrt{1+x^4}$ $x$ is a complex variable. I want to solve it for some given initial condition, and plot the solution (real part vs. imaginary part). ...
-3
votes
3answers
154 views

Gives me a complex solution [closed]

A := DSolve[{D[((It - Ir) * x / L + Ir) * w''[x], {x, 2}] - p/Y, w[x] == 0, w'[0] == 0, w''[L] == M0/(Y*Ir), w'''[L] == -P/(Y*Ir)}, w[x], x] I want a real ...
10
votes
1answer
232 views

FiniteElement v.s. TensorProductGrid: which is reliable for Schrödinger equation with periodic b.c.?

This is a problem comes up in the discussion under this post and I think it's worth starting a new question for it. I suspect the underlying issue is the same as in this post, but not sure. Consider ...
3
votes
3answers
257 views

Problem of `Integrate` and `DSolve` with inhomogeneous Legendre differential equation

I have the following inhomogeneous Legendre differential equation $(m=n=2)$: ...
7
votes
2answers
187 views

Portion of Curve Omitted by Plot

In the course of addressing question 104559, I encountered the following problem with Plot. Begin with ...
2
votes
3answers
283 views

How to take derivative of the argument of an interpolating function

I am trying to plot the derivative of the argument of an interpolating function u[t, x] with respect to $x$. Here, u[t, x] is ...
0
votes
0answers
50 views

How can I eliminate InverseLaplaceTransform returning complex

I tried this: F = InverseLaplaceTransform[ 1/((1 + s^2) (1 + (s + 1/2)^2)) + Exp[-Pi*s]*1/((1 + s^2) (1 + (s + 1/2)^2)), s, t] But it returns an answer ...
6
votes
2answers
345 views

How to solve this trigonometric complex ODE system?

The system of nonlinear ODE is $$ \mathrm{i}\,s(\ddot p-\frac{1}{2}\sin{2p}\;\dot q^2)=\mathrm{i}\,c\sin p\;\dot q-a\sin p+b\cos p\cos q\,,\\ \mathrm{i}\,s(\sin^2p\;\ddot q+\sin{2p}\;\dot p\dot q)=-\...
2
votes
2answers
181 views

DSolve Solutions are sometimes not as simple as they could be

Why doesn't DSolve output a solution in a nice format? DSolve[y'[x] == (x + y[x] + 3)^2, y[x], x] ...
3
votes
2answers
132 views

How to make an organised investigation of branch cuts from a solution to a differential equation

I am attempting to solve two differential equations. The solution gives equations that have branch cuts. I need to choose appropriate branch cuts for my boundary conditions. How do I find the correct ...
0
votes
1answer
259 views

NDSolve error (not a real number when the arguments are?)

For the NDSolve, I have problem. It seems to be non-zero imaginary part of the number. How can I get over this issue? The following is the script. ...
4
votes
1answer
419 views

Orbit followed by a particle around Schwarzschild Black Hole

The following is a equation which describes various possible orbits of a particle around the Schwarzschild black hole spacetime in general relativity. I want to solve it from ...
1
vote
0answers
133 views

Chop intermediate results of NDSolve after each step [closed]

Using NDSolve for a set of three ordinary differential equations, I ran into the problem that intermediate results quickly develop negligible imaginary parts. I get ...
0
votes
2answers
1k views

Bifurcation with a system of equations

I'm trying to plot a flip bifurcation diagram for a dynamical system of equations as follows: x'[t] == v[t] v'[t] == x[t] - A x[t]^3 + R*Cos[ω*t] - B v[t] but am ...
1
vote
0answers
79 views

Instructing DSolve not to return answers with explicit complex numbers

DSolve sometimes returns solutions containing explicit complex numbers, even though the ODE does not. For instance (drawn from question 126072), ...
5
votes
2answers
302 views

Second order differential equation of a complex function

I am curious about whether Mathematica can help me solve a second order differential equation of a function in the complex plane. The equation that I am looking to solve is: $\dfrac{d^2}{dz^2}(u+iv) ...
2
votes
1answer
174 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
9
votes
1answer
328 views

NDSolve for complex BVPs and FindRoot

NDSolve works for complex valued ODE initial value problems (IVP). However, for a simple boundary value problem (BVP) with complex coefficients it fails: ...
1
vote
1answer
337 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
2
votes
3answers
255 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
7
votes
1answer
305 views

Confirming conservation laws for complex valued functions

Consider the nonlinear Schrödinger equation (I would like to do this for a more complicated set of equations, but to gain understanding I'll consider this simplified case) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
3
votes
0answers
109 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}] ...
2
votes
1answer
3k views

Solving a complex-valued differential equation with NDSolve

I am trying to solve $dx/dt=\sqrt{1+(ix)^{1.8}}$ for initial condition $x[0] =-0.9877 + i 0.1563$, where $x$ is a complex variable. I would like to plot the imaginary part of the solution versus the ...
1
vote
0answers
813 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} &=...
5
votes
1answer
1k views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
4
votes
1answer
1k views

Real and Imaginary parts of solutions to a complex linear ODE system

Consider a complex linear ODE system $x'=Ax$, where $$A=\left( \begin{matrix} 0&1\\ -2&-i \end{matrix}\right). $$ One can first find the eigenvalues and eigenvectors using ...
3
votes
1answer
644 views

Differential Equation in Complex Plane and Parametric Plot

I would like to solve $dx/dt=\sqrt{1 + (I x)^3}$, where x is complex, for some initial condition like $1 - 5 I$ and plot the imaginary part of the solution versus the real part. (A somewhat similar ...
1
vote
2answers
862 views

Complex differential equation

I want to solve $dx/dt=\sqrt{(1-x^2)}$, where $x$ is complex. When I solve it by hand and analytically for some initial value and draw the imaginary part versus the real part, I obtain an ellipse, as ...
12
votes
1answer
5k views

Bifurcation diagrams for multiple equation systems

I am interested in constructing a bifurcation diagram for some of my parameters (especially for β and γ) in the dynamical system given in the code below. I want to see how parameter changes affect the ...