How Can Equation (13) Be Converted into the Matrix Form Ax = B?

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Discussion Overview

The discussion centers around the conversion of a specific equation, labeled as (13) in an attached document, into the matrix form Ax = B. Participants are exploring the rearrangement of this equation for iterative solving, particularly in the context of electron density calculations.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant seeks assistance in rearranging equation (13) into the form Ax = B for iterative solving.
  • Another participant asks for clarification on which variable is to be solved in equation (13).
  • The original poster specifies that they want to solve for the variable "n", which represents electron density at specific positions in a grid.
  • The original poster describes the structure of matrix "x" as containing values of "n" at various neighboring positions and matrix "B" as containing constant terms at time "t".
  • A later post reiterates the request for conversion of equation (13) into the matrix form without providing a specific method or solution.

Areas of Agreement / Disagreement

Participants generally agree on the goal of converting equation (13) into matrix form, but there is no consensus on the specific steps or methods to achieve this conversion.

Contextual Notes

The discussion does not provide details on the assumptions or definitions necessary for the conversion process, nor does it clarify any unresolved mathematical steps involved in rearranging the equation.

Gihan sky
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Please help on solving these difficult equations

In the pdf document I attached there are equations numbered (12) ,(13), (14).
These are similar equations.
I want to find a way to iteratively solve the equation number (13).
I was told that this equation can be rearranged to the form, "Ax=B".
Please help me on re-arranging the terms of this equation to this form.

Thank you.
 

Attachments

Last edited:
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You want to solve equation 13 for WHAT variable?
 
I want to solve these equation 13 for variable "n". Here n[j] is the electron density in the i,j position at time "t+1".

So the matrix "x" (if this can be rearranged to the form Ax=B) should contain the values of "n" at the positions (i,j),(i,j-1),(i,j+1),(i-1,j),(i+1,j).

matrix "B" would contain the all the constant terms at time "t".(D(E,x), R(n,p) & n[t]).

Thank you
 
Can somebody convert equation 13 into the matrix form.
i.e Ax=B
 

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