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$$ L(u)=u_{xx}+u_{yy}\quad 0<x,y<1$$ with homogenous boundary conditions.

I have tried finite difference method, $$ u_{xx}=\frac{u_{i-1,j}-2u{i,j}+u_{i+1,j}}{h^2}$$ $$ u_{yy}=\frac{u_{i,j-1}-2u{i,j}+u_{i,j+1}}{h^2}$$ Substituting in our equation, we have $$ (u_{i-1,j}-2u{i,j}+u_{i+1,j})+(u_{i,j-1}-2u{i,j}+u_{i,j+1})=0$$ after I arranged it and used BC, I got the matrix A. the steps are provided in link below in more details. https://www.physik.uzh.ch/local/teaching/SPI301/LV-2013-Help/lvanlsconcepts.chm/lvac_finite_difference_method_for_laplace_eq.html

Thank you.

Momo
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  • Welcome to MSE. Please, use descriptive titles. Your title doesn't give any idea about the subject of the question, it's useless. – jjagmath Jan 01 '21 at 20:01
  • Thank you. Can you suggest a title? because I do not know which method they used to get the matrix A. – Momo Jan 01 '21 at 20:18

1 Answers1

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It looks like the $-100$ is a misprint in $L$. Try replacing it with a $+$ sign. And make the title of the question something to do with finite differences.

Bob Terrell
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