On a modification of Newton's methods for the numerical solution of boundary problems

1963 ◽  
Vol 3 (6) ◽  
pp. 1525-1528 ◽  
Author(s):  
V.K. Isayev ◽  
V.V. Sonin
Keyword(s):  
Numerical Solution ◽  
Boundary Problems ◽  
Newton's Methods

Differential Quadrature Method in Computational Mechanics: A Review

1996 ◽  
Vol 49 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Charles W. Bert ◽  
Moinuddin Malik
Keyword(s):  
Numerical Solution ◽  
Computational Mechanics ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Solution Technique ◽  
General Interest ◽  
Quadrature Method ◽  
Physical Sciences ◽  
Boundary Problems ◽  
Potential Alternative

The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

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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