The Numerical Solution of Laplace's Equation

摘要: This paper considers in detail numerical methods of solving Laplace's equation an arbitrary two‐dimensional region with given boundary values. The involve the solution approximating difference equations by iterative procedures. Modifications standard Liebmann procedure are developed which lead to a great increase convenience and rapidity obtaining such solution. These modifications use formulas simultaneously improve block points place single point; operating on differences trial functions themselves; also method extrapolating final equations. theory underlying these procedures is considered new involves expansion error terms eigenfunctions. permits definite comparison rates convergence various techniques handling practical problems detail.