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55 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
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 ...
33 views

186 views

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

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

Problem of Integrate and DSolve with inhomogeneous Legendre differential equation

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

Portion of Curve Omitted by Plot

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

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 ...
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 ...
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 ...
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 ...