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
67 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
41 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: ...
17
votes
3answers
1k 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: ...
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 ...
4
votes
2answers
1k 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 ...
15
votes
1answer
351 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] ...
2
votes
1answer
651 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
1answer
698 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 ...
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 ...
2
votes
1answer
236 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)\,\, \...
2
votes
1answer
116 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 ...
2
votes
1answer
57 views

Difference between FourierTransform and LaplaceTransform [duplicate]

There is an equation for example: eqn=D[c[x, t], t] == d D[c[x, t], x, x]; When I make a LaplaceTransform of it: ...
0
votes
1answer
68 views

Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
0
votes
0answers
58 views

For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?

I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...