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 · by a difference quotient in the classic formulation. It is simple to code and economic to compute. In some sense, a finite difference formulation offers a more direct and intuitive approach to the numerical solution of partial differential equations than other formulations. The main drawback of the finite difference methods is the flexibility.
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