# All Questions

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### Solving complex differential equation with ParametricNDSolveValue

I am trying to solve a complex differential equation for the function $S(u,v)$ depending on the parameter $\omega$. The code is: ...
105 views

### Cryptic NDSolve::nlnum when working with matrices

This problem was initially formulated in quaternions, but I had to rewrite them to complex matrices (as they seem to be supported better). Possibly introducing some errors along the way. So the ...
43 views

### Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
190 views

### Removing numerically vanishing complex part within NDSolve [closed]

I am using functions that are only well-defined for real values (e.g. HeavisideTheta) within NDSolve. Internally ...
59 views

### How to deal with first order complex differential equation?

I am trying to solve these two equations but find an error of fewer than the dependent variable and list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. I don't ...
72 views

248 views

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

I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$ ...
144 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{\$$...
176 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). ...
177 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, w''[L] == M0/(Y*Ir), w'''[L] == -P/(Y*Ir)}, w[x], x] I want a real ...
284 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 ...
279 views

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

I have the following inhomogeneous Legendre differential equation $(m=n=2)$: ...
196 views

### Portion of Curve Omitted by Plot

In the course of addressing question 104559, I encountered the following problem with Plot. Begin with ...
507 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 ...
54 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 ...
359 views

2k 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 ...
2k 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 ...
697 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 ...
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 ...