scholarly journals Approximation Theory, Computational Mathematics and Numerical Analysis in new conception of Computational (Numerical) Diameter

2018 ◽  
Vol 124 (3) ◽  
pp. 8-88 ◽  
Author(s):  
N. Temirgaliyev ◽  
◽  
A. Zhubanysheva ◽  
Keyword(s):  
Numerical Analysis ◽  
Approximation Theory ◽  
Computational Mathematics

Peridynamics for Numerical Analysis

2021 ◽  
pp. 31-52
Author(s):  
Erdogan Madenci ◽  
Atila Barut
Keyword(s):  
Data Analysis ◽  
Numerical Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Entire Range ◽  
Numerical Solutions ◽  
Jump Discontinuity ◽  
Differentiation Process ◽  
Computational Mathematics

Discrete data analysis and numerical solutions to boundary and initial value problems of ordinary/partial differential equations are essential in almost every branch of science. Although the differentiation process is usually more direct than integration in analytical mathematics, the reverse is true in computational mathematics, especially in the presence of a jump discontinuity or a singularity. Integration is a nonlocal process because it depends on the entire range of integration. However, differentiation is a local process.

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