Transcription of FINITE DIFFERENCE METHODS FOR POISSON EQUATION
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FINITE DIFFERENCE METHODS FOR POISSON EQUATION
FINITE DIFFERENCE METHODS FOR POISSON EQUATIONLONG CHENThe best well known method, FINITE differences, consists of replacing each derivativeby a DIFFERENCE quotient in the classic formulation. It is simple to code and economic tocompute. In some sense, a FINITE DIFFERENCE formulation offers a more direct and intuitiveapproach to the numerical solution of partial differential equations than other main drawback of the FINITE DIFFERENCE METHODS is the flexibility. Standard FINITE dif-ference METHODS requires more regularity of the solution ( C2( )) and the mesh( uniform grids). Difficulties also arise in imposing boundary FINITE DIFFERENCE FORMULAIn this section, for simplicity, we discuss the POISSON EQUATION u=fposed on the unit square = (0,1) (0,1)with Dirichlet or Neumann boundary condi-tions. Recall that u= 2u x2+ 2u coefficients and more complex domains will be discussed in FINITE element meth-ods. Furthermore we assumeuis smooth enough to enable us use Taylor expansion two integersm,n 2, we construct a rectangular gridThby the tensor productof two uniform grids of(0,1):{xi= (i 1)hx,i= 1, m,hx= 1/(m 1)}and{yj= (j 1)hy,j= 1, n,hy= 1/(n 1)}.
Dec 14, 2020 · The main drawback of the finite difference methods is the flexibility. Standard finite dif-ference methods requires more regularity of the solution (e.g. u2C2()) and the mesh (e.g. uniform grids). Difficulties also arise in imposing boundary conditions. 1. FINITE DIFFERENCE FORMULA In this section, for simplicity, we discuss the Poisson ...
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