Abstract
Numerical Derivative Using the Piecewise Uniform Mesh
Highlights
Functions are known to be Stiff ( ), Its derivatives reach a certain order of that depends on the softness of the data can be limited by: | ( )( )|, ( )Where and indicates a general positive constant independent of and the number of mesh points used
This Shishkin decomposition has played a major role in finite difference analysis and finite component methods on the meshes of Shishkin and other adaptive layer meshes in recent years
The Shishkin mesh is a uniform mesh of piecewise
Summary
Its derivatives reach a certain order of that depends on the softness of the data can be limited by:. Shishkin showed that the regular and singular components of separated: have a representation of This Shishkin decomposition has played a major role in finite difference analysis and finite component methods on the meshes of Shishkin and other adaptive layer meshes in recent years. The simplest meshes are a uniform mesh * + with spaced grid points for all. With this mesh none of the mesh points will be inside the boundary layer, unless if The location of the shift point between the fine and the coarse mesh is the function of the stiffness parameter and a parameter of the discretization. A numerical comparison between Shishkin Mesh (S-Mesh) and classic Uniform Mesh (U-Mesh) will be presented, on same certain finite difference operator, in section (8)
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