# Questions tagged [numerics]

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651 questions
2k views

### Scientific computing vs numerical analysis

I'm a double major in computer science and mathematics. I love both subjects. I'm thinking in taking a graduate career, perhaps in scientific computing. What's the real difference between scientific ...
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### Is lapack getri numerically the same as getrs with identity matrix as RHS?

I was just wondering, in case of computing B=inv(A), suppose I is the identity matrix (diagonal), After obtaining the ...
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### Numerical solution to 2D divergence equation

Is there any way to numerically solve the following two-dimensional equation: $$\nabla_{xy} \cdot \vec{f}(x,y) = a(x,y)$$ on a rectangular grid, knowing that $\vec{f}(x,y)$ ...
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### Solving a second-order nonlinear ODE with a singularity on x=0

I'm doing some reasearch on electromagnetic nanostructures and I have to solve this differential equation (the exact values of the constants don't matter, I just want all the possible solutions of y(x)...
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### What is the error associated with Fornberg's algorithm?

Bengt Fornberg derived a general way to compute the weights for arbitrary finite difference schemes in two papers: his 1988 paper and (better) his 1998 paper. What are the numerical errors ...
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### Does applying the Newton-Raphson iteration for matrix reciprocal refine a matrix inverse from LU/GE?

This is a follow-up to this answer. Suppose you have a possibly very ill-conditioned matrix $A$, and you compute its inverse with LU/GE to get $X_{\text{lu}}\approx A^{-1}$. The Newton-Raphson ...
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### Classification of method for solving PDEs

If I have a system of equations as follows (where $i = \sqrt{-1}$): $$\frac {\partial A}{\partial t} = iA^*B - A \tag{1} \\$$ $$\frac {\partial B}{\partial z} = AB^* - B \tag{2}$$ Using the ...
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I have solved a PDE with an analytical equation. Through operator splitting I divided the PDE into one PDE and one ODE, using a sequential approach. Finally for different $dt$, I got euclidian norm ...
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### Numerical solution of Dirac equation (eigenvalue problem)

Suppose we have equation of the form: $$H \Psi = E \Psi$$ where $H$ is Dirac Hamiltonian (also my question can be answered by people who are not familiar with Dirac Hamiltonian but familiar with ...
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### CG question: is symmetry always necessary?

Consider the 1D Poisson equation $$\nabla^2 u = f.$$ Using finite difference method on cell corner data and a uniform grid with ghost points, I think we can write the system of equations with Neumann ...
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### Using backward difference approximations for higher order derivatives

I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of ...
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### Will the numerical solving of the differential equation be wrong if I take the step too small? [closed]

If I take the step too large I will get error, while if I take the step too small I also get an error. In my case, instead of seeing the function decreasing, i have it increasing if I take the step ...
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### Discrete conservation and Finite Element methods

What would be the rigorous mathematical expression of the fact that a conservation law discretized with a Finite Element method with Galerkin discretization does not result in a conservative scheme ?
Just studying some toy examples of $2\times 2$ and $3 \times 3$ matrices, complex number multiplication already gets a bit messy. From a numerical analysis point of view, if one were to try and build ...