On the Numerical Solution of the Dirichlet Problem for the Elliptic $$(\sigma _2)$$ ( σ 2 ) Equation

2014 ◽  
pp. 23-40 ◽  
Author(s):  
Alexandre Caboussat
Keyword(s):  
Dirichlet Problem ◽  
Numerical Solution

Approximation Schemes for Singular Integrals and Their Application to Some Boundary Problems

2004 ◽  
Vol 4 (1) ◽  
pp. 94-104
Author(s):  
Jemal Sanikidze ◽  
Manana Mirianashvili
Keyword(s):  
Dirichlet Problem ◽  
Numerical Solution ◽  
Approximate Calculation ◽  
Singular Integrals ◽  
Approximation Schemes ◽  
Cauchy Kernel ◽  
Boundary Problems ◽  
Computational Schemes

Abstract Certain schemes for approximate calculation of singular integrals with a Cauchy kernel and their application to the numerical solution of the modified Dirichlet problem are offered. Questions of justifying the corresponding computational schemes for domains with Lyapunov boundaries are investigated.

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