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Influence of several factors in the generalized finite difference method. (English) Zbl 0994.65111
Summary: It is possible to appreciate the great efficiency of the generalized finite difference method, that is to say with an irregular arrangements of nodes, to solve second-order partial differential equations which represent the behaviour of many physical processes. The method solves any type of second-order differential equation, in any type of domain and boundary condition (Dirichlet, Neumann and mixed), and immediately obtains the values of derivatives of the nodes through the application of the formulae in differences obtained.
This paper analyzes the influences of key parameters of the method, such as the number of nodes of the star, the arrangement of the same, the weight function and the stability parameter in time-dependent problems. This analysis includes solutions obtained for different types of problems, represented by different differential equations, including time-dependent equations and under different boundary conditions.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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