Linked Questions

0
votes
0answers
93 views

FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
2
votes
0answers
71 views

How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
1
vote
0answers
44 views

Fourier transform of an equation [duplicate]

I have the following equation: $$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t) $$ Which I introduced into Mathematica as: ...
19
votes
3answers
2k views

Numerically solve the initial value problem for the 1-D wave equation

I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions: ...
5
votes
2answers
2k views

Bilateral Laplace Transform

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
3
votes
2answers
3k views

Obtaining the Fourier transform of an operator

We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is $$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega} $$ and ...
7
votes
1answer
253 views

Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
2
votes
1answer
1k views

Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
5
votes
2answers
995 views

Solve PDE with DiracDelta function

This question is related to Analytic solution of dynamic Euler–Bernoulli beam equation with compatibility condition. I think it is more appropriate to open another question on this topic. In the ...
15
votes
1answer
368 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
6
votes
1answer
196 views

Derivative of real antisymmetric matrix in mathematica

Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
3
votes
2answers
158 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 ...
2
votes
1answer
259 views

How to implement the finiteness condition for a PDE?

I have a PDE $$u_t=u_{yy}+u_{zz}$$ subject to the following initial and boundary conditions $$u(y=0,z>0,t>0)=1,$$ $$u(y=0,z<0,t>0)=0,$$ $$u(y=10,z,t>0)=0,$$ $$u(y,z=\pm10,t)\,\, \...
3
votes
2answers
127 views

GreenFunction Computation for perturbed Laplacian

I am happy computing the Green function for the Laplacian Gsol := GreenFunction[{-Laplacian[u[x, y], {x, y}]}, u[x, y], {x, y} ∈ FullRegion[2], {m, n}] it gives ...
2
votes
1answer
138 views

unknown cause of scaling factors in NDSolve solutions to a partial differential equation

I am trying to solve a coupled diffusion partial differential equation with a Gaussian profile at t = 0. I would like to see how the two functions, y and z, evolve in time and in one dimension. This ...

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