On the numerical solution of n-dimensional boundary value problems associated with poisson's equation

Numerical Analysis and the Dirichlet Problem

“…The basic reason for havingmore than one method available is that there is an accumulation of truncation and roundoff error, inherent in all extensive manipulation on With the aid of these lemmas, the following theorem can be proved [23]. for points of Rh follows directly from inequality (4.2), while the proof for points of Sh follows readily from the numerical method prescribed at these points [23]. )…”

“…Other methods, also readily adaptable to today's computational machinery, which can be utilized in attempting to solve the linear system are relaxation [59], over-relaxation [70], matrix inversion [22], gradients, and conjugate gradients [28]. The basic reason for havingmore than one method available is that there is an accumulation of truncation and roundoff error, inherent in all extensive manipulation on With the aid of these lemmas, the following theorem can be proved [23]. for points of Rh follows directly from inequality (4.2), while the proof for points of Sh follows readily from the numerical method prescribed at these points [23].…”

“…Of great significance would be a rule which would enable one to determine h so that for (4. 1 which have the Laplace equation (1.1) replaced by a different elliptic differential equation [23], [24]. Finally it should be noted that the technique extends to n-dimensional problems [231, [651.…”