Questions tagged [integral-equations]
Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.
365 questions
0 votes
1 answer
130 views
Calculation of a scalar integral [closed]
I am trying to calculate the following integral using Mathematica. I have tried several times but for whatever reason I do not get a result. I am suggested to make changes that will, perhaps help with ...
- 339
0 votes
1 answer
257 views
How to avoid singularity during integration? [closed]
I applied the recommendations from my previous question, the calculation time was reduced. Thank you very much! Now I have a question regarding the calculation of some matrix elements, for example <...
- 1,933
3 votes
2 answers
300 views
Solution to a two-dimensional integration equation
I was hoping to solve a two dimensional integration equation, which is actually a simplified Schrodinger equation in momentum space: $$ (x^2-3)f(x,y)-\int_0^\infty du\int_0^{\pi}dv\frac{u^2\sin{v}f(...
- 43
8 votes
3 answers
530 views
NDSolve Integro-differential equation with memory kernel
I am trying to solve the following integro-differential equation with a memory kernel $y''(t)+a y(t)+b\int_0^t \text{d}s \, \eta(s) y'(t-s)=0,$ where the memory kernel is given by $\eta(t)=y^2(t)$, ...
- 103
0 votes
1 answer
117 views
Compute integrals in singular integral equation
I'm looking at this paper https://arxiv.org/abs/2404.07307 and in particular I am interested in eqs. (16) (17), meaning I'd like to check the validity of (16) by insert it in (17). So I'd like to ...
- 31
1 vote
0 answers
121 views
A question about integral and differential equations
I want to use Mathematica to reproduce the result of Eq.(16) under the Case I in the section 2.1 of this Article, but I failed. The result of Eq.(16) is based on differential equation Eq.(14), where, ...
- 193
1 vote
2 answers
164 views
4 votes
3 answers
330 views
Solving integral equation numerically
I tried to solve a integral equation numerically, but I failed. The equation is:$\epsilon(\beta)=r\cosh{\beta}+\int^{\infty}_{-\infty}\varphi(\beta-\beta')\ln(1+e^{-\epsilon(\beta')})d\beta'$ were $\...
