# Tagged Questions

Questions on numerical analysis/numerical methods; methods for approximately solving various problems that often do not admit exact solutions.

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### Significance of Sobolev spaces for numerical analysis & PDEs?

I never had an option to take a Functional Analysis module. I am tied up with other work for the next two months so I won't get a chance to self-study it until September. So one thing I was wondering ...
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### Please help: My MATLAB code for solving a 2D Schrödinger equation keep giving me weird output.

I've been trying to solve the following Schrödinger equation numerically, -(\frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2})\Psi + \frac{\sinh^2(y) + ...
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### error bound in function approximation algorithm

Suppose we have the set of floating point number with "m" bit mantissa and "e" bits for exponent. Suppose more over we want to approximate a function "f". From the theory we know that usually a ...
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### lattice variation, cylindrical discretisation of PDE

Given an energy functional $E=\int_{0}^{\infty} \,dr.r\left[\frac{1}{2}\left(\frac{d \phi}{dr}\right)^2 - S.\phi\right]$, I am told that discretizing on a lattice $r_{i}=ih$ (h=lattice size, i is ...
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### Simplifying the Generalized Eigenvalue Problem

Let $\Sigma_1$, $\Sigma_2$ be symmetric positive-definite real $n\times n$ matrices. We want to solve the generalized eigenvalue problem $$\Sigma_1V=\Lambda\Sigma_2V,$$ where $\Lambda$ is the ...
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